Question

The hypotenuse of a 45°-45°-90° triangle measures 7√2 units.

What is the length of one leg of the triangle?
A. 7 units
B. 7√2 units
C. 14 units
D. 14√2 units

Answer 1

The other legs are both 7 units long

Answer 2

Option A is correct.

Explanation:

Given:

Angle of the right angles triangle are 45° , 45°, 90°

Length of the Hypotenuse = 7√2 units.

To find: Length of the one leg of the triangle.

Since two angles of the triangles are equal.

⇒ Opposite sides to equal angles are also equal.

We have Isosceles right angled triangle.

⇒ both legs are equal.

Let x be the length of the leg

using Pythagoras theorem,

(7√2)² = x² + x²

2x² = 49 × 2

x² = 49

x = ±7

Length cannot be negative so, x = 7

Therefore, Option A is correct.