What is A B²+4 B Q² equal to ?

Correct Answer is : 42.25 cm242.25{ cm}²42.25 cm2

Correct Answer is : 42.25 cm242.25{ cm}²42.25 cm2

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UPSC CDS 2 2021 Math Paper

Directions (Q.Nos. 56-58) Consider the following for next three questions that follow.

A B C

is a triangle with

A B=1.6 {cm}

B C=6.3 {cm}

and

C A=6.5 {cm}

. Let

P

and

Q

be the mid-points of

A B

and

B C

respectively.

Question : 56 of 100

Marks: +1, -0

What is

A B^{2}+4 B Q^{2}

equal to ?

Solution: 👈: Video Solution

Given,

\triangle ABC, AB=1.6\text{ cm}, BC=6.3\text{ cm}

and

CA=6.5\text{ cm}

\because P

is mid-point of

AB

\therefore \;\; AP=BP

... (i)

\because Q

is mid- point of

BC

\therefore BQ=QC

\dots

(ii)

AB=1.6

\Rightarrow AP+PB=1.6

\Rightarrow PB+PB=1.6 \;\; [\because AP=BP]

\Rightarrow \;\; 2PB=1.6

\Rightarrow \;\; PB=0.8

\Rightarrow BC=6.3

\Rightarrow BQ+QC=6.3

\Rightarrow BQ+BQ=6.3 \;\; [\because BQ=QC]

\Rightarrow \;\; 2BQ=6.3 \;\; \dots

(iii)

\Rightarrow BQ=\;\frac{6.3}{2}=3.15 \;\;

... (iv)

Now,

AB^{2}+4BQ^{2}

=(1.6)^{2}+4(3.15)^{2}=2.56+4(9.9225)

=2.56+39.69=42.25\text{ cm}^{2}

Hence,

AB^{2}+4BQ^{2}=42.25\text{ cm}^{2}

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