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In a $Δ$ PQR, right angled at Q, PQ $=$ 24 cm and QR $=$ 7 cm. S is the midpoint of PR, then RS is

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3.5cm

12cm

25cm

12.5cm

answer is D.

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Detailed Solution

Given the figure,
Question Image

Given that in a

Δ

PQR, right angled at Q, PQ

=

24 cm and QR

=

7 cm and S is the midpoint of PR.
In

△ PQR

, by pythagorean theorem,

{\Rightarrow (PQ)}^{2} + {(QR)}^{2} = {(PR)}^{2}

{\Rightarrow (24)}^{2} + {(7)}^{2} = {(PR)}^{2}

\Rightarrow {(PR)}^{2} = 576 + 49

\Rightarrow {(PR)}^{2} = 625

\Rightarrow PR = 25

Now

S

is the midpoint of

PR

∴ RS = \frac{PR}{2}

\Rightarrow RS = \frac{25}{2}

\Rightarrow RS = 12.5 cm

.
Therefore,

RS = 12.5 cm

.
Hence option 4 is the answer.

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