Question

In ΔABC, AB = BC, ∠B = 90°, AC = 10 cm. Area of ΔABC is ______.

पर्याय

• 100 cm²

• 25 cm²

• 50 cm²

• 75 cm²

Answer 1

In ΔABC, AB = BC, ∠B = 90°, AC = 10 cm. Area of ΔABC is 25 cm².

Explanation:

Given: Triangle ABC is isosceles with AB = BC, angle B = 90° and hypotenuse AC = 10 cm.

Since AB = BC and angle B = 90°, triangle ABC is an isosceles right triangle, meaning AB = BC and angle B is the right angle.

For an isosceles right triangle:

Let the length of each leg AB and BC be x.

Using Pythagoras theorem:

AC² = AB² + BC²

⇒ 10² = x² + x²

⇒ 100 = 2x²

⇒ x² = 50

⇒ x = `sqrt(50)`

⇒ x = `5sqrt(2)` cm

Area of triangle ABC

= `1/2 xx AB xx BC`

= `1/2 xx x xx x`

= `1/2 xx x^2` 

= `1/2 xx 50`

= 25 cm²