You can
put this solution on YOUR website!Let x = width of original rectangle
then
x+7 = length of original rectangle
.
Then this:
"If the width is doubled and the length is increased by 2, the area is increased by 42 square units." is translated to:
(2x)(x+7+2) = x(x+7) + 42
.
Now we can solve for x:
(2x)(x+7+2) = x(x+7) + 42
(2x)(x+9) = x(x+7) + 42
2x^2 + 18x = x^2 +7x + 42
x^2 + 11x - 42 = 0
Factoring the left:
(x+14)(x-3) = 0
So,
x = {3, -14}
.
We can toss the negative solution leaving us with:
x = 3 units (width of original rectangle)
.
length:
x+7 = 3+7 = 10 units (length of original rectangle)
.
ANS: dimension of original rectangle: 3 units by 10 units
