Question

The sides of a rectangle are in the ratio 4:7. If its longer side is 31.5 in., find the shorter side, the perimeter, and the area of this rectangle.

Answer 1

Answer:

Width = 18 inches

Perimeter = 99 inches

Area = 567 square inches

Step-by-step explanation:

The sides of a rectangle are in the ratio 4:7. Then

Width $=4x$ in

Length $=7x$ in.

If  its longer side is 31.5 in, then

Length = 31.5 in

and

$7x=31.5\\ \\x=\dfrac{31.5}{7}=4.5\ in$

So,

Width $=4\cdot 4.5=18\ in$

The perimeter is

$P=2(\text{Width}+\text{Length})\\ \\=2(18+31.5)\\ \\=2\cdot 49.5\\ \\=99\ in$

The area is

$A=\text{Width}\cdot \text{Length}\\ \\=18\cdot 31.5\\ \\=567\ in^2$