In ‖ gm ABCD, it is given that AB = 10cm, DL ⊥ AB and BM ⊥ AD such that DL = 6cm and BM = 8cm. Then, AD = ?

Question

Philoid · Accepted Answer

Given:

AB = 10cm

DL ⊥ AB

BM ⊥ AD

DL = 6cm

BM = 8cm

Now, consider the parallelogram ABCD

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

Area of the parallelogram is given by: Base × Height

∴ area of ‖gm ABCD = AB×DL = 10×6 = 60cm²

Now,

Consider AD as base of the parallelogram then BM becomes its altitude (height)

∴ area of ‖gm ABCD = AD × BM = 60cm²

AD × 8 = 60cm²

AD = 60/8 = 7.5cm

∴length of AD = 7.5cm.

In ‖gm ABCD, it is given that AB = 10cm, DL ⊥ AB and BM ⊥ AD such that DL = 6cm and BM = 8cm. Then, AD = ?