Question

In a parallelogram ABCD, AB=14cm, the altitude corresponding side AB and AD are 8cm & 7cm respectively. Find AD

20cm
16
24cm
None​

Answer 1

Given:-

• In a parallelogram ABCD, AB = 14cm
• The altitude corresponding side AB and AD are 8 cm and 7 cm respectively.

To Find:-

The measure of AD

Construction:-

Draw two perpendiculars. The 1st perpendicular line for AD and the 2nd perpendicular line for AB. And name them as E and F respectively.

Note:-

Refer to the attachment for the diagram.

Solution:-

We know that the area of a parallelogram is Base × Height sq.units

So for this parallelogram we have two bases:-

1st base = AB = 14 cm

2nd Base = AD = ?

The Area of the parallelogram will remain the same.

Therefore,

AD × DF = AB × BE

= $\sf{AD \times 7 = 14 \times 8}$

= $\sf{AD = \dfrac{14\times8}{7}}$

= $\sf{AD = 2\times 8}$

$\sf{AD = 16\:cm}$

Therefore the measure of AD is 16 cm.

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More about Parallelogram:-

• Parallelogram is a quadrilateral which has two of its sides parallel.
• Sum of it's adjacent side is always 180°
• Each pair of diagonals of a parallelogram divides it into two congruent triangles.
• The formula of area of a parallelogram is Base × Height sq.units.

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