In the diagram, P Q R is a right-angled triangle with ≤ft|P R|=15\;{cm} and ≤ft|Q R|=12\;{cm}. Find the length P Q.

Correct Answer is : 9.0 cm\;\;9.0\;{cm}9.0cm

Correct Answer is : 9.0 cm\;\;9.0\;{cm}9.0cm

Test Index

BECE Mathematics 2018 Paper

Question : 23

Total: 40

P Q R

\left|P R\right|=15\;\text{cm}

\left|Q R\right|=12\;\text{cm}

P Q

Solution:

Concept:

Use Pythagoras theorem for a right-angled triangle.

Explanation:

\triangle PQR

, the right angle is at

Q

So, the hypotenuse is

PR = 15\;\text{cm}

By Pythagoras theorem:

PR^2 = PQ^2 + QR^2

Substitute the given lengths:

15^2 = PQ^2 + 12^2

Therefore,

225 = PQ^2 + 144

Subtract

144

from both sides:

225 - 144 = PQ^2

This gives

81 = PQ^2

Taking the positive square root:

PQ = \sqrt{81} = 9\;\text{cm}

Answer:

PQ = 9.0\;\text{cm}

, which is option C.

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