The length of a rectangle is 5 more than the width and the area is 24. Find the length and the width.
Solution
The formula of the area of a rectangle is
A = L * w
Translate the phrase "The length of a rectangle is 5 more than the width" into an equation.
We get: L = w + 5
Replace A by 24 and replace L by w + 5
24 = (w + 5) * w
24 = w^{2} + 5w
24  24 = w^{2} + 5w  24
0 = w^{2} + 5w  24
Factor the expression on the right
0 = ( w + blank) * ( w + blank)
To get blank, look for factors of 24 that will add up to 5.
8 * 3 = 24 and 8 + 3 = 5
So fill in the blank with 8 and 3
0 = (w + 8) * ( w + 3)
Now solve the above
w + 8 = 0
w + 3 = 0
w + 8 = 0
w + 8  8 = 0 8
w = 8. The answer cannot be negative
w + 3 = 0
w + 3 + 3 = 0 + 3
w = 3
L = w + 5 = 3 + 5 = 8
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