Correct Answer - Option 4 : 12 cm
Given:
A right-angled triangle.
Sides of triangle = (x + 5) cm
(x - 4) cm
(x + 3) cm
Formula used:
In right angled triangle;
(Hypotenuse)2 = (Base)2 + (Perpendicular)2
Calculation:
∵ (x + 5) is the biggest side.
∴ (x + 5)2 = (x - 4)2 + (x + 3)2
⇒ x2 + 25 + 10x = x2 + 16 - 8x + x2 + 9 + 6x
⇒ x2 + 25 + 10x = 2x2 - 2x + 25
⇒ 2x2 - 2x + 25 - x2 - 25 - 10x = 0
⇒ x2 - 12x = 0
x2 = 12x
⇒ x = 12
∴ Value of x is 12
