Question

Farmer Brown wants to double the size of his rectangular backyard vegetable patch by adding a strip (of the same width) all the way around it. If its current patch is 12 feet by 18 feet, how wide does the strip need to be?

how do you solve it step by step ?

Answer 1

A1 = 12 * 18=216Ft^2=Area of 1st patch.
Add X Ft to each side:

A2 = (12 + X)(18 + X) = 2*216 = 432Ft^2
= Area of 2nd patch.

216 + 12X + 18X + X^2 = 432,
X^2 + 30X + 216 = 432,
X^2 + 30X + 216 - 432 = 0,
X^2 + 30X -216 = 0,

X = (-30 +- sqrt(900 + 864)) / 2,
X = (-30 +- 42) / 2,
X = 6, and X = -36,
Select positive value of X:
X = 6 Ft Wide.

Answer 2

X=3