Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

$text In a Triangle end text A B C comma less than B less than 90 to the power of ring operator text and end text A D text is drawn perpendicular to end text B C text . Prove that end text A C squared equals A B squared plus B C squared minus 2 B C. B D$

hint Hint:

Hint :- Applying pythagoras theorem to both triangles ABD and ADC. find the AD2 from both equations substitute value of AD2 .Equate both the equations to get the required condition .

The correct answer is: Hence proved

Aim :- Prove that $A C squared equals A B squared plus B C squared minus 2 B C times B D$
Explanation(proof ) :-
As angle b is acute the perpendicular line AD lies inside the triangle
Applying pythagoras theorem in ΔACD ,We get
$A C squared equals A D squared plus C D squared$ — Eq1
Applying pythagoras theorem in ΔABD ,We get
$A B squared equals B D squared plus A D squared not stretchy rightwards double arrow A D squared equals A B squared minus B D squared$ —Eq2
Substitute Eq1 in Eq2 ,
$A C squared equals A B squared minus B D squared plus C D squared not stretchy rightwards double arrow A C squared equals A B squared plus C D squared minus B D squared$

$text By using end text a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis text and end text B C equals B D plus C D text we get, end text$

$not stretchy rightwards double arrow A C squared equals A B squared plus left parenthesis B D plus C D right parenthesis left parenthesis C D minus B D right parenthesis$
$open not stretchy rightwards double arrow A C squared equals A B squared plus B C left parenthesis left parenthesis C D plus B D right parenthesis minus 2 B D right parenthesis close parentheses left parenthesis AddCD text and subtract end text CD right parenthesis$
$not stretchy rightwards double arrow A C squared equals A B squared plus B C left parenthesis B C minus 2 B D right parenthesis$
$therefore A C squared equals A B squared plus B C squared minus 2 B C times B D$
Hence proved

Related Questions to study

Simplify √12 - √48 +√1323

Simplify √12 - √48 +√1323

In $straight triangle A B C$ , the bisectors of $straight angle A B C$ and $straight angle B C A$ intersect each other at O. Prove that $straight angle B O C equals$ $90 to the power of ring operator plus 1 half straight angle A$

In $straight triangle A B C$ , the bisectors of $straight angle A B C$ and $straight angle B C A$ intersect each other at O. Prove that $straight angle B O C equals$ $90 to the power of ring operator plus 1 half straight angle A$

and are the medians of a $straight triangle ABC$ right angled at . Prove that $4 open parentheses BL squared plus C straight C squared close parentheses equals 5 BC squared$ .

and are the medians of a $straight triangle ABC$ right angled at . Prove that $4 open parentheses BL squared plus C straight C squared close parentheses equals 5 BC squared$ .

parallel

In $straight triangle space ABC$ right angled at A, AL is drawn perpendicular to BC. Prove that $straight angle BAL equals straight angle ACB$ .

In $straight triangle space ABC$ right angled at A, AL is drawn perpendicular to BC. Prove that $straight angle BAL equals straight angle ACB$ .

Simplify √50 - √98 + √162

Simplify √50 - √98 + √162

A fish tank is in the shape of a cube . Its volume is 125 Cubic feet . What is the area of one face of the tank ?

A fish tank is in the shape of a cube . Its volume is 125 Cubic feet . What is the area of one face of the tank ?

parallel

In the adjacent figure, points B, A, D are collinear and AD = AC.
Given that $straight angle space BAC equals 50 to the power of ring operator$ and $straight angle B C D equals 80 to the power of ring operator$ . Find $straight angle space ABC space text and end text straight angle space ACB$ .

In the adjacent figure, points B, A, D are collinear and AD = AC.
Given that $straight angle space BAC equals 50 to the power of ring operator$ and $straight angle B C D equals 80 to the power of ring operator$ . Find $straight angle space ABC space text and end text straight angle space ACB$ .

In the figure, ABC is a triangle in which $A D perpendicular B C$ . Show that $A C squared equals A B squared plus B C squared minus 2 B C times B D$
.

In the figure, ABC is a triangle in which $A D perpendicular B C$ . Show that $A C squared equals A B squared plus B C squared minus 2 B C times B D$
.

Solve the equation m² = 14

Solve the equation m² = 14

parallel

The traversers are adding a new room to their house. The room will be a cube with a volume of 6589 cubic feet .They are going to put in hardwood floors , which costs Rs 10 per square foot . How much will the hardwood floors cost ?

The traversers are adding a new room to their house. The room will be a cube with a volume of 6589 cubic feet .They are going to put in hardwood floors , which costs Rs 10 per square foot . How much will the hardwood floors cost ?

$text In a Triangle end text A B C comma less than A equals 90 to the power of ring operator text and end text A D text is drawn perpendicular to end text B C text . Prove that end text A B squared plus C D squared equals B D squared plus A C squared$

$text In a Triangle end text A B C comma less than A equals 90 to the power of ring operator text and end text A D text is drawn perpendicular to end text B C text . Prove that end text A B squared plus C D squared equals B D squared plus A C squared$

The angles of a triangle are $left parenthesis x minus 40 right parenthesis to the power of ring operator comma left parenthesis x minus 20 right parenthesis to the power of ring operator text and end text open parentheses x over 2 minus 10 close parentheses$ Find the value of and then the angles of the triangle

The angles of a triangle are $left parenthesis x minus 40 right parenthesis to the power of ring operator comma left parenthesis x minus 20 right parenthesis to the power of ring operator text and end text open parentheses x over 2 minus 10 close parentheses$ Find the value of and then the angles of the triangle

parallel

D and E are points on the base BC of $straight triangle space ABC$ such that BD = CE. If AD = AE, prove that $straight angle ABE equals straight angle ACD$ .

D and E are points on the base BC of $straight triangle space ABC$ such that BD = CE. If AD = AE, prove that $straight angle ABE equals straight angle ACD$ .

Sita has a square shaped garage with 228 square feet of floor space. She plans to build an addition that will increase the floor space by 50%. What will be the length of one side of new garage ?

Sita has a square shaped garage with 228 square feet of floor space. She plans to build an addition that will increase the floor space by 50%. What will be the length of one side of new garage ?

$A B C D text is a rhombus, prove that end text A C squared plus B D squared equals 4 times A B squared$

$A B C D text is a rhombus, prove that end text A C squared plus B D squared equals 4 times A B squared$

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.