Question

In the quadrilateral ABCD, AB = 7 cm, BC = 17 cm, AD = CD = x. ∠B = 90° = ∠D.

The value of x is ______.

Options

• 13 cm

• 15 cm

• 12 cm

• 16 cm

Answer 1

The value of x is 13 cm.

Explanation:

In the quadrilateral ABCD,

AB = 7 cm, BC = 17 cm, AD = CD = x, ∠B = ∠D = 90°

We need to find the value of x.

In ΔABC,

By Pythagoras theorem,

AC² = AB² + BC²

AC² = 7² + 17²

= 49 + 289

= 338

AC = `sqrt(338)`

In ΔADC,

Again by Pythagoras theorem,

AC² = AD² + DC²

338 = x² + x²

338 = 2x²

x² = `338/2`

x² = 169

x = `sqrt(169)`

x = 13 cm