Answers are
a) w=52 m
b) L = 97 cm
Step by step
a) the perimeter is 278m, the length is 87m.
We are looking for the width.
We know the formula is P= 2L + 2W
So
278 = (2)(87) + 2W
278 = 174 + 2W
Subtract 174 from both sides to isolate variable
278-174 = 174 -174 + 2W
Combine
104 = 2W
Divide both sides by 2 to solve
104/2 = 2/2 W
52 = W
Check your work
278 = (2)(87) + (2)(52)
278 = 174 + 104
278 = 278
Problem solved!
b) Area of the window is 7081 cm^2, width is 73cm. We are looking for length.
We know the formula for area is
A = L x W
So
7081 = L x 73
Divide both sides by 73 to solve
7081/73 = L x 73/73
97 cm = Length
Check your work
7081 = 97 x 73
7081 = 7081
Problem solved!