Question

perimeter of a rectangle is 2.4 meter less than 2/5 of perimeter of a square. if the perimeter of the square is 40 meter; find the length and breadth of the rectangle given that breath is 1/3 of the length.

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Answer 1

Answer

First, we should find the perimeter of the rectangle.

Perimeter of the rectangle :

$\sf \dashrightarrow \bigg( \dfrac{2}{5} \: of \: 40 \bigg) - 2.4$

$\sf \dashrightarrow \bigg( \dfrac{2}{5} \times 40 \bigg) - 2.4$

$\sf \dashrightarrow \bigg(\dfrac{2 \times 40}{5} \bigg) - 2.4$

$\sf \dashrightarrow \bigg( \dfrac{80}{5} \bigg) - 2.4$

$\sf \dashrightarrow 16 - 2.4$

$\sf \dashrightarrow Perimetre = 13.6$

Now, we can find the length of the rectangle by the formula of perimetre of the rectangle.

Length of the rectangle :

Let the length of the rectangle be y.

Let the breadth of the rectangle b ⅓ of y.

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

$\sf \dashrightarrow 13.6 = 2 \: \bigg(y + \dfrac{1}{3} \: of \: y \bigg)$

$\sf \dashrightarrow 13.6 = 2 \: \bigg(y + \dfrac{1}{3} \times y \bigg)$

$\sf \dashrightarrow 13.6 = 2 \: \bigg( y + \dfrac{1y}{3} \bigg)$

$\sf \dashrightarrow 13.6 = 2 \: \bigg( \dfrac{3y + 1y}{3} \bigg)$

$\sf \dashrightarrow 13.6 = 2 \: \bigg( \dfrac{4y}{3}\bigg)$

$\sf \dashrightarrow \dfrac{4y}{3} = \dfrac{13.6}{2}$

$\sf \dashrightarrow \dfrac{4y}{3} = 6.8$

$\sf \dashrightarrow 4y = 6.8 \times 3$

$\sf \dashrightarrow 4y = 20.4$

$\sf \dashrightarrow y = \dfrac{20.4}{4}$

$\sf \dashrightarrow y = 5.1 \: m$

Now, let's find the breadth of the rectangle.

Breadth of the rectangle :

$\sf \dashrightarrow \dfrac{1}{3} \: of \: 5.1$

$\sf \dashrightarrow \dfrac{1}{3} \times 5.1$

$\sf \dashrightarrow \dfrac{1 \times 5.1}{3} = \dfrac{5.1}{3}$

$\sf \dashrightarrow \cancel \dfrac{5.1}{3} = 1.7$

Hence, the length and breadth of the rectangle are 5.1 and 1.7 metres respectively.