Question

The area of a parallelogram is 72 sqare centi meter and its altitude is twice the corresponding base .then the length of the base is dash

Answer 1

GIVEN:

• The area of a parallelogram is 72 cm²
• Its altitude is twice the corresponding base.

TO FIND:

• What is the length of the base of parallelogram ?

SOLUTION:

Let the length of the parallelogram be 'b' and height of parallelogram be 'h' cm

✒ We have given that the height is twice the base

➵ h = 2b....1)

To find the area of parallelogram, we use the formula:-

❰ AREA = BASE $\times$ HEIGHT ❱

According to question:-

➵ 72 = b $\times$ 2b (From equation 1)

➵ 72 = 2b²

➵ $\sf{\cancel\dfrac{72}{2}}$ = b²

➵ 36 = b²

➵ $\sf{\sqrt{36}}$ = b

➵ 6 cm = b

Put the value of 'b' in equation 1)

➵ h = 2 $\times$ 6

➵ h = 12 cm

❝ Hence, the base of parallelogram is 6 cm and the height of parallelogram is 12 cm ❞

______________________

Answer 2

★ Given : The area of a parallelogram is 72 sqare centi meter and its altitude is twice the corresponding base.

$\rule{130}1$

★ Solution :

$\begin{lgathered}\bullet\:\:\textsf{Area of parallelogram = \textbf{72 sq.cm}}\\\bullet\:\:\textsf{Height = \textbf{2b}}\end{lgathered}$

$\rule{170}2$

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies\sf Area_{(parallelogram)} = base \times height \\\\\\:\implies\sf 72 = b \times 2b\:\:\:\:\:\:\: \Big\lgroup \bf{ \because h = 2b}\Big\rgroup \\\\\\:\implies\sf 2b^2 = 72 \\\\\\:\implies\sf b^2 = 36\\\\\\:\implies\sf b = \sqrt{36} \\\\\\:\implies\underline{\boxed{\sf Base = 6}}$

$\therefore\:\underline{\textsf{The length of base is \textbf{6 cm}}}.$