Question

in a parallelogram ABCD, AB=20cm , the altitude corresponding to the sides AB and AD are respectively 7cm and 8cm . Find AD

1) 87.5cm
2)8.75cm²
3)17.5cm
d) none of these
​

Answer 1

The length of AD is 17.5 cm.

Step-by-step explanation:

Referring to the figure attached below, we have,  

ABCD is a parallelogram  

AB = 20 cm  

The altitude corresponding to side AB = 7 cm  

The altitude corresponding to side AD = 8 cm

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

Area = Base × Altitude

Firstly, we have  

Side AB = 20 cm and let the altitude corresponding to this side be CM which is 7 cm.  

∴ Area = AB × CM = 20 × 7 = 140 cm²  

Now, considering the side AD, let the corresponding altitude to this side be CN which is 8 cm.  

∴ Area = AD × CN

⇒ 140 = AD × 8  

⇒ AD =  $\frac{140}{8}$

⇒ AD = 17.5 cm  ← option (3)

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