Question

The height of a parallelogra. is one fourth of its base.If its area is 144sq. cm.then find its breadth and height.
​

Answer 1

Here is your answer...

Area of pallgm.= b× h

let the base be x .

and the height be 1/4 of x .

144 = x × 1/4 x

144 = 1/4x²

1/4x²= 144

x² = 144 ÷ 1/4

x² = 144 × 4

x² =576.

so, base is 576 and height is 2× 576.

Answer 2

$\textbf{\underline{\underline{Answer :-}}}$

The Height is 6 cm and Base is 24 cm

$\textbf{\underline{\underline{Explanation :-}}}$

Given :

Height of the Parallelogram = one fourth of its base.

Area = 144 sq.cm

To find :

It's breadth and height.

Solution :-

Consider the base as x

Height = $\sf{\dfrac{1x}{4}}$

We know that :

$\boxed{\sf{Area = Height\times Base}}$

$\sf{\implies} \: 144 = x\:\times \dfrac{1x}{4}$

$\sf{\implies} \: x \times \dfrac{1x}{4}= 144$

$\sf{\implies} \:{x}^{2}= 144 \times 4$

$\sf{\implies} \:{x}^{2}=576$

$\sf{\implies} \: x =\sqrt{576}$

$\sf{\implies} \: x = 24$

Base = 24 cm

Value of $\sf{\dfrac{1x}{4}}$

$\sf{\implies} \:\dfrac{1}{4}\times 24$

$\sf{\implies} \: 1 \times 6$

$\sf{\implies}6$

$\boxed{\sf{\red{Base = 24 \: cm}}} \\ \boxed{\sf{\red{Height = 6\: cm}}}$

$\therefore$ The Height is 6 cm and Base is 24 cm

$\textbf{\underline{\underline{Verification :-}}}$

$\sf{\implies} \: 24 \times 6$

$\sf{\implies}144$

$\therefore$ The Height is 6 cm and Base is 24 cm