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 [tex]=4x[/tex] in
Length [tex]=7x[/tex] in.
If its longer side is 31.5 in, then
Length = 31.5 in
and
[tex]7x=31.5\\ \\x=\dfrac{31.5}{7}=4.5\ in[/tex]
So,
Width [tex]=4\cdot 4.5=18\ in[/tex]
The perimeter is
[tex]P=2(\text{Width}+\text{Length})\\ \\=2(18+31.5)\\ \\=2\cdot 49.5\\ \\=99\ in[/tex]
The area is
[tex]A=\text{Width}\cdot \text{Length}\\ \\=18\cdot 31.5\\ \\=567\ in^2[/tex]
