Question

A square and a parallelogram have the same area if the side of the square is 48 m and the height of the parallelogram is 18 m find the length of the base of the parallelogram

Answer 1

GIVEN:

• Area of square is same as the area of parallelogram.
• Side of square = 48 m
• Height of parallelogram = 18 m

TO FIND:

• What is the length of the base of the parallelogram ?

SOLUTION:

Let the length of the base of parallelogram be 'b' m

We have given that, the area of square is same as the area of parallelogram.

❰ (Side)² = BASE $\times$ HEIGHT ❱

According to question:-

On putting the given values in the formula, we get

➸ (48)² = b $\times$ 18

➸ 2304 = 18b

➸ $\sf{\cancel\dfrac{2304}{18}}$ = b

❰ 128 m = b ❱

❝ Hence, the length of the base of the Parallelogram is 128 m ❞

______________________

Answer 2

Given : A square and a parallelogram have the same area if the side of the square is 48 m and the height of the parallelogram is 18 m.

$\rule{130}{1}$

Solution :

$\underline{\bigstar\:\textbf{According to the Question :}}$

$\dashrightarrow\sf\:\:Area\: of\: square = a \times a\\\\\\\dashrightarrow\sf\:\: 48 \times 48\\\\\\\dashrightarrow\color{aqua}\sf\:\: 2304\:m$

$\rule{130}{1}$

$\dashrightarrow\sf\:\:Area\: of\: parallelogram = base \times height\\\\\\\dashrightarrow\sf\:\: b \times 18\\\\\\\dashrightarrow\color{aqua}\sf\:\: 18b$

$\rule{130}{1}$

$:\implies\sf Area \:of \:square = Area\:of\: parallelogram \\\\\\:\implies\sf 18b = 2304\\\\\\:\implies\sf b = \dfrac{2304}{18}\\\\\\:\implies\underline{\boxed{\sf Base = 128\:m}}$⠀

$\therefore\:\underline{\textsf{The length of the base of the parallelogram is \textbf{128 m}}}.$

$\rule{170}{2}$