Question

In a right angled triangle, if sum of the squares of the sides making right angle is 169 then what is the length of the hypotenuse?Select the correct alternative.
(A) 15
(B) 13
(C) 5
(D) 12

Answer 1

Answer:

(B) 13

Step-by-step explanation:

As per the question,

We have been provided that the sum of the squares of the sides making right angle is 169.

As we know that according to Pythagoras theorem,

Sum of the square of two sides containing right angles is always equal to square of the third side that is also hypotenuse.

If PQR is the right triangle at ∠Q = 90°

∴ PQ² + QR² = PR²

Using this concept, we can find the value of third side

PQ² + QR² = PR²

169 = PR²

∴ PR = 13

Hence, the length of third side = 13.

Therefore, correct option is (B).

Answer 2

Answer:

Hence, the length of the hypotenuse is 13.

Step-by-step explanation:

As per the data provided in above question.

The given data is as follows.

Sum of the square of the sides making right angle is 169.

We have to find the length of the hypotenuse.

According to the Pythagoras Theorem,

Sum of the square of the two side of right angles is always equal to the square of third i.e. Hypotenuse.

Suppose, if ΔABC is right angle.

$AB^{2}$+$BC^{2}$=$AC^{2}$

We have the sum of the square of the both sides is 169.

i.e. $AB^{2}$+$BC^{2}$=169

∴$AC^{2}$=169

Taking square root on both side.

$=\sqrt{13\times13}$

AC=13

Hence, the length of the hypotenuse is 13.