Problema Solution
The area of a rectangle is 200 square cm. If the perimeter is 60 cm, find the length and width of the rectangle.
Answer provided by our tutors
Perimeter = 2×Length + 2×Width
Area = Length×Width
60 = 2L + 2W
200 = LW
Splve the first equation for W and substitute in the second equation:
60 = 2L + 2W
Divide through by 2
30 = L + W
30 - L = w
Substitute (30 - L) for W in
200 = LW
200 = L(30 - L)
200 = 30L - L²
Get 0 on the right:
L² - 30L + 200 = 0
Factor the left side:
(L - 20)(L - 10) = 0
Use the zero-factor property:
L - 20 = 0; L - 10 = 0
L = 20; L = 10
Subdtitute in
30 - L = w 30 - L = w
30 - 20 = W 30 - 10 = W
10 = W 20 = W
We usually think of the length as the longer side, so
the length is 20 and the width is 10