Question

In the quadrilateral ABCD, ∠B = 90° = ∠D, AB = 7 cm, BC = 17 cm and AD = DC = x. Find the value of x.

Answer 1

In the quadrilateral ABCD,

∠B = 90° and ∠D = 90°

AB = 7 cm

BC = 17 cm

AD = DC = x

We are asked to find the value of x.

Step 1: Use Pythagoras theorem in ΔABC:

AC² = AB² + BC²

AC² = 7² + 17²

AC² = 49 + 289

AC² = 338

AC = `sqrt(338)`

AC ≈ 18.4 cm

Step 2: Use Pythagoras theorem in ΔACD:

AC² = AD² + DC²

AC² = x² + x²  ...(Since AD = DC = x)

AC² = 2x²

338 = 2x²   ...(Taking AC² value from step 1)

x² = `338/2`

x² = 169

x = `sqrt(169)`

x = 13 cm