Question

The length of three sides of a triangle is x, (x + 7) and (x + 8). If the triangle is right angle triangle, what is the value of x?

1. 8
2. 5
3. 15
4. 10

Answer 1

Correct Answer - Option 2 : 5

Given:

length of three sides of a triangle is x, (x + 7) and (x + 8)

Concept:

⇒ (hypotenuse)² = (base)² + (perpendicular)²

Calculation:

According to the question,

⇒ (x + 8)² = (x + 7)² + x²

⇒ x² + 16x + 64 = x² + 14x + 49 + x²

⇒ x² – 2x – 15 = 0

⇒ x² – 5x + 3x – 15 = 0

⇒ x(x – 5) + 3(x – 5) = 0

⇒ (x – 5) (x + 3) = 0

⇒ x = 5 or – 3

∴ Value of x = 5    …… (∵ x, length of a side cannot be negative)