Question

The length of two sides of a right angle triangle is 5 cm and 12 cm, then the length of the third side will be ------ cm. *

17 सेमी

7 सेमी

13 सेमी

25 सेमी​

Answer 1

Answer:

13cm

By the Pythagoras theorem

H²=B²+A²

H²=12²+5²

H²=169

H=√169

H=13cm

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Answer 2

Correct Question :-

‣ The length of two sides of a right angle triangle is 5 cm and 12 cm, then the length of the third side will be ___ cm. *  

1.) 17 cm

2.) 7 cm

3.) 13 cm

4.) 25 cm

Answer :-

Option 3.) 13 cm is the correct answer.

Given :-

→ The length of the first side = 5 cm

→ The length of the second side = 12 cm

To find :-

• The length of third side (or hypotenuse)

Solution :-

Let the third side be h.

As it is given in the question that the triangle is a right angled triangle. So, we will use Pythagoras Theorem to find the length of third side.

$\star$ According to Pythagoras Theorem,

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

$\boxed{\longrightarrow \tt{(Hypotenuse)^{2} = (First\:\:side)^{2} +(Second\:\:side)^{2}} }$

Now, Substituting the values we have in this formula.

$=> \tt{(h)^{2} = (5\:\:cm)^{2} +(12\:\:cm)^{2}} \\\\=> \tt{(h)^{2} = 25\:\:cm^{2} +144\:\:cm^{2}}\\\\=> \tt{(h)^{2}} = 169\:\:cm^{2}}\\\\=> \tt{h = \sqrt{169\:\:cm^{2}}}\\\\=> \tt{h =13\:\:cm}}$

Therefore, the length of the third side = 13 cm.