SOLUTION: 2. If each side of a square is increased by 2 cm, the total area of both the new square and the original square will be 400 cm2. Approximate to the nearest tenth of a centimeter t

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: 2. If each side of a square is increased by 2 cm, the total area of both the new square and the original square will be 400 cm2. Approximate to the nearest tenth of a centimeter t      Log On

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Question 575465: 2. If each side of a square is increased by 2 cm, the total area of both the new square and the
original square will be 400 cm2. Approximate to the nearest tenth of a centimeter the length of
each side of the original square.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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2. If each side of a square is increased by 2 cm, the total area of both the new square and the original square will be 400 cm2.
Approximate to the nearest tenth of a centimeter the length of each side of the original square.
:
let x = side of the smaller square
then
(x+2) = side of the larger square
:
(x+2)^2 + x^2 = 400
FOIL
x^2 + 4x + 4 + x^2 - 400 = -
Combine like terms
2x^2 + 4x - 396 = 0
Simplify, divide by 2
x^2 + 2x - 198 = 0
Use the quadratic formula to find
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=1; b=2; c=-198
x+=+%28-2%2B-+sqrt%282%5E2-4%2A1%2A-198+%29%29%2F%282%2A1%29+
do the math here, the positive solution:
x = 13.1 cm
:
:
Check this by finding the area of each square
13.1^2 = 171.61
15.1^2 = 228.01
----------------
total A: 399.62 ~ 400