Question

The perimeter of a parallelogram is 40 cm. If its longer side measures 13cm, what is the measure of its shorter side?

Answer 1

the measure of the shorter side is 7cm

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Answer 2

• The measure of the shorter side (height) of the parallelogram = 7 cm.

Diagram :

$\setlength{\unitlength}{8mm}\begin{picture}(6, 6)\put(1,1){\line(3,4){2}}\put(1,1){\line(4,0){4.5}}\put(5.5,1.1){\line(4,5){2}}\put(3,3.6){\line(4,0){4.5}}\put(4.4,4){\sf{13 cm}}\put(3.2,2.2){\sf\small{{P = 40\:cm}}}\put(7,2){\sf{x}}\end{picture}$

Given :

• The perimeter of a parallelogram = 40 cm.
• The measure of the longer side = 13 cm.

To Find :

• The measure of the shorter side of the parallelogram.

Solution :

Let,

The shorter side (height) of the parallelogram be x.

Given,

The perimeter of the parallelogram = 40 cm.

We know that,

The perimeter of the parallelogram = 2 ( a + b )

Where,

• a = height.
• b = base.

We have,

Base = 13 cm.

That means,

→ 2 ( a + b ) = 40 cm --------(1)

→ 2 ( x + 13 cm ) = 40 cm

→ x + 13 cm = 40 / 2 cm

→ x + 13 cm = 20 cm

→ x = 20 cm – 13 cm

→ x = 7 cm

x = height = shorter side = 7 cm

Hence,

The measure of the shorter side (height) of the parallelogram is 7 cm.

Verification :

Now we have,

The perimeter of the parallelogram is 40 cm.

The longer side of the parallelogram is 13 cm.

From equation (1),

→ 2 ( a + b ) = 40 cm

Where,

• a = height = 7 cm.
• b = base = 13 cm.

→ 2 ( 7 cm + 13 cm ) = 40 cm

→ 2 ( 20 cm ) = 40 cm

→ 2 × 20 cm = 40 cm

→ 40 cm = 40 cm

Hence Verified !