Question

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




please solve this​

Answer 1

Option (B)

Given :-

In a right angled triangle, if the sum of the squares of the sides making right angle is 169.

To find :-

The length of the hypotenuse .

Solution :-

Given that

The sum of the squares of the other two sides in a right angled triangle = 169

Let the length of the hypotenuse of the triangle be X units

We know that

By Pythagoras Theorem

Hypotenuse ² = Sum of the squares of the other two sides

=> X² = 169

=> X = ± √169

=> X = ± 13

X can't be negative.

Since, The length of the side must be a positive integer.

=> X = 13 units

Therefore, X = 13 units

Answer :-

The length of the hypotenuse of the right angled triangle is 13 units

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,

sum of the squares of the sides making right angle is 169.

find the length of hypotonuse

Solution :

Let the Length hypotonuse be x cm .

By Pythagoras theorem,

$\boxed{ \color{gold} \tiny \bf {hypotonuse}^{2} = sum \: of \: squares \: of \: \: other \: \: two \: \: sides}$

so, on substituting the value

$\rm⇢ \: \: {x}^{2} = 169$

$\rm⇢ \: \: x = \sqrt{169}$

$\rm⇢ \: \: x = \pm13$

$\tt⇢ \: \:x = 13cm \: \: \: ( \because \: length \: cannot \: \: be - ve)$

FINAL ANSWER :

The length of hypotonuse is 13cm .

Hence, option (B) is the correct answer .