In the figure given, $∠ P S R = 90^{o}$ , PQ $= 10$ cm, $Q S = 6$ cm and RQ $= 9$ cm. Calculate the length PR.

16 c m

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17 c m

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18 c m

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19 c m

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Solution

The correct option is B $17 c m$
$I n △ P Q S$
$B y p y t h a g o r a s t h e o r e m,$

${P S}^{2} + {S Q}^{2} = {P Q}^{2}$

$⟹ {P S}^{2} = {P Q}^{2} - {S Q}^{2}$

$⟹ {P S}^{2} = 10^{2} - 6^{2}$

$⟹ {P S}^{2} = 100 - 36 = 64$

$⟹ P S = 8$

$I n △ P S R$
$⟹ {P S}^{2} + {R S}^{2} = {P R}^{2} (p y t h a g o r a s)$

$⟹ {P R}^{2} = {P S}^{2} + {R S}^{2}$

$⟹ {P R}^{2} = 64 + {(R Q + Q S)}^{2} = 64 + 15^{2}$

$⟹ {P R}^{2} = 64 + 225$

$⟹ {P R}^{2} = 289$

$⟹ P R = 17 c m$

Suggest Corrections

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In the figure: PQ = 10 cm, QS = 6 cm and RQ = 9 cm.
The length of side PR is.

In the figure: $∠ P S Q = 90^{\circ},$
PQ = 10 cm, QS = 6 cm and RQ = 9 cm.
Calculate the length of PR.

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