Question

find the length of the hypotenuse of a right angle triangle if remaining side are 9 cm and 12 cm.​

Answer 1

Answer :-

• The hypotenuse of the right angled triangle is 15 cm.

To find :-

• The length of the hypotenuse of a right angled triangle whose remaining sides are 9 cm and 12 cm.

Step-by-step explanation :-

• Here, the other two sides of a right angled triangle are given to us. We have to find the length of it's hypotenuse.

We know that :-

• In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Here,

• The other two sides are 6 cm and 12 cm.

Therefore,

$\longmapsto\sf Hypotenuse^2 = 9^2 + 12^2$

$\sf \longmapsto Hypotenuse^2 = 81 + 144$

$\sf \longmapsto Hypotenuse^2 = 225$

$\sf \longmapsto Hypotenuse = \sqrt{225}$

$\longmapsto \underline{\boxed{\sf Hypotenuse = 15 \: cm}}$

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• Hence, the hypotenuse of the right angled triangle is 15 cm.

Answer 2

$\huge \maltese \sf \: {given}$

$\bold{ \dagger \: base \: and \: perpendicular = 9 \: cm \: \: and \: 12 \: cm}$

$\huge \sf \underbrace \color{blue}{formulae}$

$\bold{ \leadsto \: ( {hypotenuse})^{2} = ({base})^{2} + ({perpendicular})^{2}}$

$\sf \hookrightarrow \: {(hypotenuse)}^{2} = {9}^{2} + {12}^{2}$

$\sf \hookrightarrow \: {(hypotenuse)}^{2} = 81 + 144 = 225$

$\sf\hookrightarrow \: hypotenuse = \sqrt{225}$

$\underline \bold{ \longmapsto \: hypotense = 15}$

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