Maths-
General
Easy
Question
Hint:
Hint :- let the side of equilateral triangle be x , then we get height of equilateral triangle as
.Now , Find length of DE and apply pythagoras theorem in Right angle triangle ADE to find length of AD in terms of AB.
The correct answer is: Hence proved
Aim :- Prove that ![9 A K squared equals 7 A C squared](data:image/png;base64,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)
Explanation(proof ) :-
BK:KC = 2:1 KC :( KC+BK) = 1:(1+2) KC :CB = 1:3
In equilateral triangle all sides are equal
Let , AB = BC = CA = x
Given CK =
BC =
( BC is trisected at K)
In equilateral triangle ,the altitudes and medians coincide
so,AE is median also i.e E is midpoint of BC
CE = ![X over 2](data:image/png;base64,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)
From diagram ,KE = CE - CK =![x over 2 minus x over 3 equals x over 6](data:image/png;base64,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)
We get height of equilateral triangle when side x is ![fraction numerator x square root of 3 over denominator 2 end fraction](data:image/png;base64,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)
![](data:image/png;base64,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)
Applying pythagoras theorem on triangle ADE
We get, ![A K squared equals E K squared plus A E squared equals open parentheses x over 6 close parentheses squared plus open parentheses fraction numerator x square root of 3 over denominator 2 end fraction close parentheses squared](data:image/png;base64,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)
![A K squared equals x squared over 36 plus fraction numerator 3 x squared over denominator 4 end fraction equals fraction numerator 28 x squared over denominator 36 end fraction equals 7 over 9 x squared](data:image/png;base64,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)
Substitute x by AC as x = AC
![A K squared equals 7 over 9 A C squared not stretchy rightwards double arrow 9 A K squared equals 7 A C squared](data:image/png;base64,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)
Hence proved
Related Questions to study
Maths-
The perpendicular AD on the base BC of Triangle ABC intersects BC in D such that BD = 3CD. Prove that
![2 A B squared equals 2 A C squared plus B C squared](data:image/png;base64,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)
The perpendicular AD on the base BC of Triangle ABC intersects BC in D such that BD = 3CD. Prove that
![2 A B squared equals 2 A C squared plus B C squared](data:image/png;base64,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)
Maths-General
Maths-
In an equilateral
the side BC is trisected at D . Prove that ![9 A D squared equals 7 A B squared](data:image/png;base64,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)
.
In an equilateral
the side BC is trisected at D . Prove that ![9 A D squared equals 7 A B squared](data:image/png;base64,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)
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Maths-General
Maths-
![](data:image/png;base64,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)
ABC and DBC are two isosceles triangles on the same base BC. Show
that ![straight angle ABD equals straight angle ACD](data:image/png;base64,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)
![](data:image/png;base64,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)
ABC and DBC are two isosceles triangles on the same base BC. Show
that ![straight angle ABD equals straight angle ACD](data:image/png;base64,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)
Maths-General
Maths-
PQ and RS are respectively the smallest and longest sides of a quadrilateral PQRS. Show that ∠ P > ∠ R
PQ and RS are respectively the smallest and longest sides of a quadrilateral PQRS. Show that ∠ P > ∠ R
Maths-General
Maths-
Classify whether the following Surd is rational or irrational , justify. 3√24− 5√5
Classify whether the following Surd is rational or irrational , justify. 3√24− 5√5
Maths-General
Maths-
In △ABC, AD and are the bisectors of ∠A and ∠C respectively. AD and CE intersect at . If ∠ABC = 90^∘, then find ∠AOC.
In △ABC, AD and are the bisectors of ∠A and ∠C respectively. AD and CE intersect at . If ∠ABC = 90^∘, then find ∠AOC.
Maths-General
Maths-
Maths-General
Maths-
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
Maths-General
Maths-
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.
Maths-General
Maths-
Maths-General
Maths-
Classify whether the following Surd is rational or irrational , justify 8-√48
Classify whether the following Surd is rational or irrational , justify 8-√48
Maths-General
Maths-
Classify whether the following Surd is rational or irrational , Justify.√47+√8
Classify whether the following Surd is rational or irrational , Justify.√47+√8
Maths-General
Maths-
In the figure, sides QP and RQ of a
are produced to points S and T respectively.
If
and
, find
.
![](data:image/png;base64,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)
In the figure, sides QP and RQ of a
are produced to points S and T respectively.
If
and
, find
.
![](data:image/png;base64,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)
Maths-General
Maths-
Simplify √8 - √18 + √50
Simplify √8 - √18 + √50
Maths-General
Maths-
Maths-General