Question

A book cover has the length and width(in inches) shown in the diagram.
A) Find the values of a and b
B) Find the perimeter of the book cover.
Widths are top--3b in. bottom--(2+a)in.
Lengths are left--(3a-b) in. And right--(2+a+2b) in.

Answer 1

as you know, perimeter is 2(length+width)

With no actual numbers provided, it is impossible to assign values to a and b.

Answer 2

"Widths are top--3b in. bottom--(2+a)in."
⇒
3b=2+a

"Lengths are left--(3a-b) in. And right--(2+a+2b) in."
⇒
3a-b=2+a+2b

Solve for a and b, hence perimeter.
Hint: both a and b are positive, and are both integers.

Answer 3

You have your two equations.

3b = 2+a
3a-b = 2+a+2b

rearrange things a bit and you have

a - 3b = -2
2a - 3b = 2

subtract and you have
a=4
so, b=2

Answer 4

game on