Question

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

Answer 1

Given:

• The length of a rectangle is 8 cm more than 3 times it's width.
• Perimeter of rectangle is 64 cm.

To Find:

• What will the equation for finding the dimensions of rectangle?

Solution: Let the width of rectangle be x cm. Therefore,

• Length of rectangle = 8 more than 3 time of width = (3x + 8) cm

★ Perimeter of rectangle = 2(Length + Width) ★

But Perimeter = 64 cm given

A/q

• Equation = 64 = 2(3x + 8 + x)

$\implies{\rm }$ 64 cm = 2 ( 3x + 8 + x ) cm

$\implies{\rm }$ 64 cm = 2 ( 4x + 8) cm

$\implies{\rm }$ 64 cm = 8x + 16 cm

$\implies{\rm }$ ( 64 – 16 ) cm = 8x

$\implies{\rm }$ 48 cm = 8x

$\implies{\rm }$ 48/8 cm = x

$\implies{\rm }$ 6 cm = x

Hence, The width of rectangle = x = 6 cm and

Length of rectangle = (3x + 8) = 3(6) + 8 = 26 cm