rectangle word problem
the length of a rectangle is 5 more than the width and the area is 24. Find the length and the width.
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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