Question

the length and width of the rectangle are in the ratio 4:3. if the perimeter of the rectangle is 56 m, find the length and width of the rectangle​

Answer 1

Given

• The length and width of the rectangle are in the ratio 4:3
• Perimeter of rectangle is 56 m

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To Find

• The length and width of rectangle

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Solution

Let the length be 4x and width be 3x (Here we have taken it as 4x and 3x since they are in the ratio of 4:3)

Formula to Find the Perimeter of Rectangle → 2 (Length + Width)

Perimeter of Given Rectangle → 56 m

Let's solve the below equation step-by-step to find the length and width of the rectangle.

2 (4x + 3x) = 56

Step 1: Simplify the equation.

⇒ 2 (4x + 3x) = 56

⇒ 2 (7x) = 56

⇒ 14x = 56

Step 2: Divide 14 from both sides of the equation.

⇒ 14x ÷ 14 = 56 ÷ 14

⇒ x = 4

∴ Length of Rectangle → 4x = 4(4) = 16 m

∴ Width of Rectangle → 3x = 3(4) = 12 m

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Answer 2

${\bf{Given\::}}$

• The length and width of a rectangle are in the ratio 4 : 3.

• The perimeter of the rectangle is 56 m.

$\\ {\bf{To\: Find\::}}$

• The length and width of the rectangle.

$\\ {\bf{Solution\::}}$

Let,

• Length of the rectangle is 4x.

• Width of the rectangle is 3x.

As we know that,

➣ Perimeter of the rectangle is given as,

$\orange\bigstar\:{\Large\mid}\:\bf\purple{Perimeter_{(rectangle)}\:=\:2\:(Length\:+\: Width)\:}\:{\Large\mid}\:\green\bigstar$

➠ 56 = $\tt{2\:(4x\:+\:3x)}$

➠ 56 = $\tt{2\times{7x}}$

➠ $\tt{14x}$ = 56

➠ x = $\tt{\dfrac{56}{14}}$

➠ x = $\bf\red{4}$

Hence,

• Length = 4x = 4 × 4 = 16 m

• Width = 3x = 3 × 4 = 12 m

∴ The length and width of the rectangle are 16 m & 12 m respectively.