Question

if the perimeters of a rectangle is 140 cm and breadth of it is 3/4 of it's length what is the area of the rectangle​

Answer 1

Answer

To find the area of the rectangle, first we should be known with the length and breadth. So, let's find the lengths be breadth first.

Let the length of the rectangle be y.

Let the breadth of the rectangle be ¾ of y.

Now, let's find the value of length by using the formula of rectangle's perimetre.

Length of the rectangle :

$\sf \dashrightarrow {Perimetre}_{(Rectangle)} = 2\: (Length + Breadth)$

$\sf \dashrightarrow 140 = 2 \bigg( y + \dfrac{3}{4} \: of \: y \bigg)$

$\sf \dashrightarrow 140 = 2 \bigg( y + \dfrac{3}{4} \times y \bigg)$

$\sf \dashrightarrow 140 = 2 \bigg( y + \dfrac{3y}{4} \bigg)$

$\sf \dashrightarrow 140 = 2 \bigg( \dfrac{4y + 3y}{4} \bigg)$

$\sf \dashrightarrow 140 = 2 \bigg( \dfrac{1y}{4} \bigg)$

$\sf \dashrightarrow 140 = \dfrac{2y}{4}$

$\sf \dashrightarrow \dfrac{2y}{4} = 140$

$\sf \dashrightarrow \dfrac{1y}{2} = 140$

$\sf \dashrightarrow 1y = 140 \times 2$

$\sf \dashrightarrow y = 28$

Now, we can find the breadth of the recatngle.

Breadth of the rectangle :

$\sf \dashrightarrow \dfrac{3}{4} \: of \: y$

$\sf \dashrightarrow \dfrac{3}{4} \: of \: 28$

$\sf \dashrightarrow \dfrac{3}{4} \times 28$

$\sf \dashrightarrow \dfrac{3 \times 28}{4} = \dfrac{84}{4}$

$\sf \dashrightarrow \dfrac{84}{4} = 21$

Now, we can find the area of the recatngle by it's formula.

Area of the rectangle :

$\sf \dashrightarrow Length \times Breadth$

$\sf \dashrightarrow 28 \times 21$

$\sf \dashrightarrow {588 \: cm}^{2}$

Hence, the area of the rectangle is 688 cm².