Question

In a parallelogram ABCD ,AB=8cm . the lengths of altitudes corresponding to AB and AD are 4cm and 5cm respectively. Find the length of AD.​

Answer 1

If AB is 8 cm and length of altitudes are 4 cm & 5 cm then the length of AD is 6.4 cm.

Step-by-step explanation:

Referring to the figure attached below, we have,

ABCD is a parallelogram

AB = 8 cm

DM = altitude corresponding to side AB = 4 cm

BN = altitude corresponding to side AD = 5 cm

We know that the formula of the area of a parallelogram is given by,

Area = Base × Altitude

Firstly, we have

Side AB = 8 cm and the altitude corresponding to this side, DM which is 4 cm.

∴ Area = AB × DM = 8 × 4 = 32 cm²

Now, considering the side AD, the corresponding altitude of this side, BN which is 5 cm.

∴ Area = AD × BN

⇒ 32 =  AD × 5

⇒ AD =  $\frac{32}{5}$

⇒ AD = 6.4 cm

Thus, the length of AD is 6.4 cm.

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Answer 2

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