Question

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The hypotenuse of a right triangle is 17 cm long . If one of the remaining two sides is of length 8 cm , Find the length of the third side .​

Answer 1

Step-by-step explanation:

Given :-

The hypotenuse of a right triangle is 17 cm long . If one of the remaining two sides is of length 8 cm

To find :-

Find the length of the third side ?

Solution :-

Given that

The hypotenuse of a right angled triangle = 17 cm

Length of the One of the remaining two sides

= 8 cm

Let the third side be a cm

We have,

b = 8 cm

c = 17 cm

We know that

By Pythagoras Theorem,

Hypotenuse² = Side² + Side²

=> c² = a²+b²

=> 17² = a²+8²

=> 289 = a² + 64

=> 289-64 = a²

=> 225 = a²

=> a² = 225

=> a = ±√225

=> a = ±15

=> a = 15 cm

Since the length of the side cannot be negative.

The third side = 15 cm

Answer:-

The length of the third side of the right angled triangle is 15 cm

Used Theorem :-

Pythagoras theorem :-

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

Answer 2

Given :-

In a triangle,

• The hypotenuse is 17 cm
• Another side is 8 cm

To Find :-

• The length of the third side ?

Used Formula :-

♣️ Pythagoras Theorem :

$\implies \bf \: \red{Hypotenuse^{2} = Base^{2} +Height^{2} }$

Step-by-step Explanation :-

Given that,

➸ The Hypotenuse = 17

➸ Another side = 8

➸ Third side = x

Substituting those values,

$\: : \implies \: \sf \: Hypotenuse^{2} = Base^{2} +Height^{2}$

$\: : \implies \: \sf \: 17^{2} \: = \: 8^{2} +Height^{2}$

$\: : \implies \: \sf \: 17^{2} \: = \: 8^{2} +x^{2}$

$\: : \implies \: \sf \: 289\: = \: 64 +x^{2}$

$\: : \implies \: \sf \: 289 - 64\: = \: x^{2}$

$\: : \implies \: \sf \: 225\: = \: x^{2}$

$\: : \implies \: \sf \: 15\: = \: x$

$\: : \implies \: \bf \red{\: x\: = \: 15}$

Hence,

The third side of a triangle is 15 cm .

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