SOLUTION: the area of a rectangle is 270cm2. if the shorter side was teduced by 2cm and the longer side was increased by 4 cm. then the area would be increased by 16cm2. find the length of

Question 1102354: the area of a rectangle is 270cm2. if the shorter side was teduced by 2cm and the longer side was increased by 4 cm. then the area would be increased by 16cm2. find the length of sides of the original rectangle?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
the area of a rectangle is 270cm2
L * w = 270.
if the shorter side was teduced by 2cm and the longer side was increased by 4 cm. then the area would be increased by 16cm2
(L+4)*(w-2) = 270 + 16
FOIL
Lw - 2L + 4w - 8 = 286
We can replace Lw with 270
270 - 2L + 4w - 8 = 286
-2L + 4w + 262 = 286
-2L + 4w = 286 - 262
-2L + 4w = 24
simplify, divide by 2
-L + 2w = 12
2w - 12 = L
In the first equation, replace L with (2w-12)
(2w-12)*w = 270
form a quadratic equation
2w^2 - 12w - 270 = 0
simplify, divide by 2
w^2 - 6w - 135 = 0
You can use the quadratic formula, a=1; b=-6; c= -135, but this will factor
(w - 15)(w + 6) = 0
two solutions, we want the positive one
w = 15 cm is the width
find the length
270/15 = 18 cm is the length (the original rectangle)
:
:
Check this by finding the area when length is 22 cm and width is 13 cm
22 * 13 = 286, which is 16 more than the original area
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