Question

the base of a parallelogram is twice its height if the area of the parallelogram is 200 CM square find the perimeter of the parallelogram
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Answer 1

• Given

• The base of the parallelogram is twice its height.
• Area of the parallelogram = 200 cm²

• To find

• Perimeter of the parallelogram

• Concept

We are given the value of the area of the parallelogram. Firstly, we will let the height of the parallelogram and then we will let the base of the parallelogram twice its height. By using the formula of area of parallelogram we will find the base and height. And then by using the formula to find perimeter of the parallelogram we will find its value.

• Solution

Let the height of the parallelogram be x and the base of the parallelogram be 2x.

Usi g formula,

Area of the parallelogram = b × h

where,

• b = base of the parallelogram
• h = height of the parallelogram

Substituting the values,

⟶ 200 = x × 2x

⟶ 200 = 2x²

⟶ 200/2 = x²

⟶ 100 = x²

⟶ √100 = x

⟶ ± 10 Reject - ve = x

The value of x = 10

• The base of parallelogram = 2x = 2 × 10 = 20 cm
• The height of parallelogram = x = 10 cm

Using formula,

Perimeter of parallelogram = 2(a + b)

where,

• a = side of the parallelogram
• b = base of the parallelogram

Substituting the values,

⟶ 2(20 + 10)

⟶ 2(30)

⟶ 60 cm

Therefore, the perimeter of the parallelogram is 60 cm.