Let ABCD be a ‖ gm in which DL ⊥ AB and BM ⊥ AD such that AD = 6 cm, BM = 10 and DL = 8 cm. Find AB.

Question

Philoid · Accepted Answer

Given:

AD = 6cm

DL ⊥AB

BM ⊥ AD

DL = 8cm

BM = 10cm

Now, consider the parallelogram ABCD

Here, let AD be the base of the parallelogram then BM becomes its altitude (height).

Area of the parallelogram is given by: Base × Height

∴ area of ‖gm ABCD = AD×BM = 6×10 = 60cm²

Now,

Consider AB as base of the parallelogram then DL becomes its altitude (height)

∴ area of ‖gm ABCD = AB × DL = 60cm²

AB × 8 = 60cm²

AB = = 7.5cm

∴length of AB = 7.5cm.