Question

The height of the parallelogram is one fourth of its base. if the area of the parallelogram is 676sq.cm,find the height and the base.

Answer 1

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$\large\blue{Solution:-}$

Let the base of the parallelogram be x cm. So, height = 4x cm

Area of the parallelogram = Base × Height = x × 4x = 4x^2 sq.cm

According to the question,

4x^2 = 676

x^2 = 676/4

x^2 = 169

x = (169)^1/2

x = 13 cm

So,

Base = 13 cm

Height = 52 cm

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Answer 2

The base of parallelogram is "52 cm" and height is "13 cm".

Explanation:

$Let \ the \ base \ of \ parallelogram \ be \ "x".\\\\The \ height \ be \ "\frac{1}{4}x".\\\\Area,A=676 \ cm^2\\\\As \ we \ know,\\\\The \ Area \ of \ parallelogram,\\A=base\times height\\\\676=x\times \frac{1}{4}x\\ \\2704=x^2\\\\x=\sqrt{2704}\\ \\x=52\\\\Now,\\The \ base \ of \ parallelogram=52 \ cm\\The \ height \ of \ parallelogram=\frac{1}{4}\times 52=13 \ cm$

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