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

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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:

From pythagoras theorem

The hypotenuse (

c

) is the side facing the right-angle. The longest side of the triangle.

\;15^2=12^2+\left|P Q\right|^2

\;225=144+\left|P Q\right|^2

\;225-144=\left|P Q\right|^2

\;81=\left|P Q\right|^2

A number when multiplied by itself, will give 81, which is 9

9 \times 9=\left|P Q\right|^2

Every number is raised to the power 1

9^1 \times 9^1=\left|P Q\right|^2

From the law of indices,

a^m \times a^n=a^{m+n}

\;9^{1+1}=\left|P Q\right|^2

\;9^2=\left|P Q\right|^2

Since the powers are the same, the bases should also be the same

9=\left|P Q\right|

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