A triangle $Δ$ PQR with $∠ Q = 90^{\circ}$ , QR = 8 cm and PR = 10 cm is constructed. What would be the measure of PQ?

3 cm

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4 cm

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10 cm

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6 cm

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Solution

The correct option is D 6 cm
Given $∠ Q = 90^{\circ}$ , which means that the sides PQ and QR are the sides and PR is the hypotenuse of the right angle triangle. Using Pythagoras theorem, we get
$P R^{2} = P Q^{2} + Q R^{2}$
$\Rightarrow 10^{2} = P Q^{2} + 8^{2}$
$\Rightarrow P Q^{2} = 10^{2} - 8^{2}$
$\Rightarrow P Q^{2} = 100 - 64$
$\Rightarrow P Q^{2} = 36$
$\Rightarrow P Q = 6$

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A triangle Δ PQR with ∠Q=90∘, QR = 8 cm and PR = 10 cm is constructed. What would be the measure of PQ?

The correct option is D 6 cmGiven ∠Q=90∘, which means that the sides PQ and QR are the sides and PR is the hypotenuse of the right angle triangle. Using Pythagoras theorem, we get PR2=PQ2+QR2 ⇒102=PQ2+82 ⇒PQ2=102−82 ⇒PQ2=100−64 ⇒PQ2=36 ⇒PQ=6

A triangle $Δ$ PQR with $∠ Q = 90^{\circ}$ , QR = 8 cm and PR = 10 cm is constructed. What would be the measure of PQ?