Question

The sum of the squares of sides of a right-angled triangle is 8,450 square units. What is the length of its hypotenuse?
1. 50 units
2. 55 units
3. 60 units
4. 65 units

Answer 1

Correct Answer - Option 4 : 65 units

Given:

The sum of the squares of sides of a right-angled triangle is 8,450 square units.

Concept Used:

In right-angle ΔABC,

If ∠B = 90° 

Then by using pythagorus theorem,

(Hypotenuse)² = (Pependicular)² + (Base)²

AC² = AB² + BC²

Calculation:

Let the sides of the right-angled triangle be “a” and “b” units respectively.

If “h” is the length of the hypotenuse,

Then according to the concept used,

⇒ a² + b² = h²      ----(1)

Now, it is given that the sum of the squares of sides of a right-angled triangle is 8,450 square units.

a² + b² + h² = 8450      ----(2)

Now from equation (1) and (2),

2h² = 8450

⇒ h² = 8450/2

⇒ h² = 4225

⇒ h = 65.

∴ The length of hypotenuse is 65.