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

$A B C text is a right triangle with end text straight angle A equals 90 to the power of ring operator BL text and end text CM text are its medians. Prove that end text 4 open parentheses BL squared plus CM squared close parentheses equals 5 BC squared text . end text$

The correct answer is: Hence proved

Solution :-
Aim :- Prove that $4 open parentheses B L squared plus C M squared close parentheses equals 5 B C squared$
Hint :- Applying pythagoras theorem to both triangles ACM and BLA. find the BL²
and CM² add them and substitute proper conditions to prove the condition .
Explanation(proof ) :-
Given, BL and CM are the medians of a triangle ABC
M is midpoint of AB i.e AM = ½ AB
L is mid point of AC i.e AL = ½ AC
Applying pythagoras theorem to triangle BLA we get ,
$B L squared equals A L squared plus A B squared$
As we know AL = ½ AC we get $B L squared equals A B squared plus fraction numerator A C squared over denominator 4 end fraction minus Eq 1$
Applying pythagoras theorem to triangle ACM we get ,
$C M squared equals A C squared plus A M squared$
As we know AM = ½ AB we get $C M squared equals A C squared plus fraction numerator A B squared over denominator 4 end fraction minus Eq 2$ — Eq2
Applying pythagoras theorem to triangle ABC we get ,
$A B squared plus A C squared equals B C squared minus Eq 3$

Adding Eq1 and Eq2 we get ,
$B L squared plus C M squared equals A B squared plus fraction numerator A C squared over denominator 4 end fraction plus A C squared plus fraction numerator A B squared over denominator 4 end fraction$
$not stretchy rightwards double arrow B L squared plus C M squared equals 5 over 4 open parentheses A B squared plus A C squared close parentheses$
Substitute Eq 3 in the above , we get
$B L squared plus C M squared equals 5 over 4 open parentheses B C squared close parentheses not stretchy rightwards double arrow 4 open parentheses B L squared plus C M squared close parentheses equals 5 B C squared$
Hence proved

Related Questions to study

Classify whether the following Surd is rational or irrational , justify 4√5+ 9

Classify whether the following Surd is rational or irrational , justify 4√5+ 9

PQR is a triangle in which PQ=PR.S is any point on the side PQ. Through S, a line is drawn parallel to QR intersecting PR at T. Prove that PS = PT.

PQR is a triangle in which PQ=PR.S is any point on the side PQ. Through S, a line is drawn parallel to QR intersecting PR at T. Prove that PS = PT.

$text In Triangle end text A B C text , If end text A D text is the median show that, end text A B squared plus A C squared equals 2 open parentheses A D squared plus B D squared close parentheses$

$text In Triangle end text A B C text , If end text A D text is the median show that, end text A B squared plus A C squared equals 2 open parentheses A D squared plus B D squared close parentheses$

parallel

Classify whether the following Surd is rational or irrational , justify 8-√48

Classify whether the following Surd is rational or irrational , justify 8-√48

Classify whether the following Surd is rational or irrational , Justify.√47+√8

Classify whether the following Surd is rational or irrational , Justify.√47+√8

In the figure, sides QP and RQ of a $straight triangle P R R$ are produced to points S and T respectively.
If $straight angle SPR equals 135 to the power of ring operator$ and $straight angle POT equals 110 to the power of ring operator$ , find $straight angle PRQ$ .

In the figure, sides QP and RQ of a $straight triangle P R R$ are produced to points S and T respectively.
If $straight angle SPR equals 135 to the power of ring operator$ and $straight angle POT equals 110 to the power of ring operator$ , find $straight angle PRQ$ .

parallel

Simplify √8 - √18 + √50

Simplify √8 - √18 + √50

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

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

Prove in the given figure, side QR of a $straight triangle space PQR$ is produced to a point S.
If the bisector of $straight angle PQR$ and $straight angle PRS$ meet at the point T, then prove
$straight angle QTR equals 1 half straight angle QPR$

Prove in the given figure, side QR of a $straight triangle space PQR$ is produced to a point S.
If the bisector of $straight angle PQR$ and $straight angle PRS$ meet at the point T, then prove
$straight angle QTR equals 1 half straight angle QPR$

parallel

In an equilateral triangle ABC,D is a point on the side BC , such that $BD equals 1 third BC$ . Prove that
$9 AD squared equals 7 AB squared$

In an equilateral triangle ABC,D is a point on the side BC , such that $BD equals 1 third BC$ . Prove that
$9 AD squared equals 7 AB squared$

In the figure, find the value of x.

In the figure, find the value of x.

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

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

parallel

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

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.