Question

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

Answer 1

Answer:

52 cm and 13 cm respectively.

Explanation:

Let base be x cm.

So height become $1/4x$

Given

Area of the parallelogram is 676 sq.cm

We know

Area of the parallelogram = Base × Height

Now put the put here

$\displaystyle x\times1/4x=676\\\\\displaystyle x\times x=676\times4\\\\\displaystyle x^2=676\times4\\\\\displaystyle x=\sqrt{676\times4}\\\\\displaystyle x=26\times2\\\\\displaystyle x=52$

Thus base of the parallelogram is 52 cm

Height of the parallelogram is 52 × 1 / 4 = 13 cm.

Verification:

Area of the parallelogram = Base × Height

Put the values here

R.H.S. = Base × Height

R.H.S. = 52 × 13

R.H.S. = 676 sq.cm

Already area is given 676 sq.cm

L.H.S. = R.H.S

Hence verified.

Answer 2

$\bf\huge\underline\red{Answer}$

Given:

Let the base of the parallelogram be x cm.

$\bf\large{Height\: of\: the \:parallelogram\: =1/4x}$ $\bf\underbrace{the\: height\: of \:the\: parallelogram \:is\: one \:fourth\: of\: its\: base.}$

$\bf\boxed{Area\:of\: the \:parallelogram \:=676 sq.cm}$

$\bf\huge\boxed{Solution}$

$\bf\huge\boxed{Area\: of\: a\: parallelogram\:=\:Base × Height }$

Substitute the values of the base and height of the parallelogram in the above formula.

676 = x × $\bf\frac{1}{4x}$

x × x = 676 × 4

x² = 2704

x = √2704

x = 52

Base of the parallelogram = x = 52cm

Height of the parallelogram = x $\bf\huge\frac{1}{4}$

Height of the parallelogram = 52 × 1/4

Height of the parallelogram = 13cm

•°• Base of the parallelogram = 52cm

Height of the parallelogram = 13 cm

$\bf\huge\boxed{Verification}$

Area of parallelogram = B × H

$\bf\underbrace{B= base, H = height }$

$\bf{676 = 13 × 52}$$\bf\large\underbrace{Area \:of \:the\: parallelogram \:given \:as\: 676sq.cm}$

676 = 676

LHS = RHS.

Hence verified.