Answer:
31 cm
Explanation:
First, we choose two variables.
Let W = width.
Let L = length.
The perimeter of a rectangle is:
perimeter = 2(L + W)
Now we translate the statements of the problem into two equations.
"the perimeter is 178 cm"
2(L + W) = 178
Divide both sides by 2:
L + W = 89
"the length of a rectangle is 4 cm less than the twice of the width"
L = 2W - 4
We have a system of equations:
L + W = 89
L = 2W - 4
Rewrite the first equation:
L + W = 89
Since the second equation is already solved for L, we can easily use the substitution method.
Substitute 2W - 4 for L in the equation above.
2W - 4 + W = 89
Combine like terms on the left side.
3W - 4 = 89
Add 4 to both sides.
3W = 93
Divide both sides by 3.
W = 31
Answer: The width is 31 cm
Check:
The length is 4 cm less than twice the width. 2 × 31 cm - 4 cm = 58 cm
The length is 58 cm, and the width is 31 cm. Calculate the perimeter.
P = 2(L + W) = 2(58 cm + 31 cm) = 2(89 cm) = 178 cm
The perimeter is 178 cm as the problem states, so the answer, width = 31 cm, is correct.