Answer:
width is 25 inches
length is 31 inches
Step-by-step explanation:
We will need the formula for perimeter of a rectangle:
P = 2(l + w)
"l" is length, "w" is width
If the length exceeds the width by 6, then:
l = w + 6 <= Substitute this into the equation
P = 2(l + w)
P = 2(w + 6 + w)
Remember we also know the perimeter is 112:
112 = 2(w + 6 + w)
Collect like terms:
112 = 2(2w + 6)
Start isolating "w" to find width.
56 = 2w + 6 Divided both sides by 2
50 = 2w Subtracted 6 from both sides
25 = w Divided both sides by 2
w = 25 Variable on left for standard formatting
The width is 25 inches.
Find the length using "length exceeds width by 6".
l = w + 6
l = 25 + 6 Substitute the width
l = 31
The length is 31 inches.
∴ The length is 31 inches and the width is 25 inches.
Check your answer with the perimeter formula.
P = 2(l + w)
112 = 2(31 + 25) Substitute all the variables.
112 = 2(56)
112 = 112 Same answer
LS = RS Left side equals right side
The answer is correct.
