Question

The length of a rectangle is 8cm more then 3 times its width. The perimeter of the rectangle is 64cm. Show the equationd that would be used to find the dimensions of the rectangle

Answer 1

Let the width be x

Length = 8cm more than 3 times the width

Length = 8 + 3x

Perimeter = 64

Perimeter of rectangle = 2(l + b)

Substitute the values,

2(8 + 3x + x) = 64

This is the required equation.

On solving the equation,

2(8 + 3x + x) = 64

16 + 6x + 2x = 64

16 + 8x = 64

8x = 64 - 16

8x = 48

x = 48/8

x = 6

To find length and breadth,

Breadth = x = 6cm

Length = 8 + 3x

= 8 + 3(6)

= 8 + 18

= 26cm

Answer 2

Let the length and breadth of the rectangle be x and y respectively.

Given

The length of a rectangle is 8 cm more then 3 times its width.

$\implies x=3y+8\\\implies x-3y=8$

The perimeter of the rectangle is 64 cm.

$\implies 2(x+y)=64$

$\implies 2(3y+8+y)=64$

$\implies 2(4y+8)=64$

$\implies 4y+8 = 32$

$\implies 4 y = 32-8$

$\implies 4y=24$

$\implies y = \dfrac{24}{4}$

$\implies y = 6$

$\implies x = 3y+8\\\implies x = 18+8\\\implies x = 26$

Therefore, the length and breadth of the rectangle are 26 cm and 6 cm respectively.