Find the length of a side of each of two squares given that the sum of their perimeters is 44 ft and the sum of their areas is 73 ft2.
2006-12-31 04:13:11 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
8 and 3
2006-12-31 04:34:53 · answer #1 · answered by Mena M 3 · 0⤊ 0⤋
We'll just use a polynomial to solve this problem:
x^2 + y^2 = 73 and
y = 1/4 of 44 minus x so
x^2+((0.25(44)-x)^2)=73
Now solve this polynomial by factoring and reducing:
x^2 + (11-x)(11-x) = 73
x^2 + 121 - 22x + x ^2 = 73
2x^2 - 22x + 121 = 73
2x^2 - 22x = -48
x^2 - 11x + 24 = 0
This is the standard format for a solvable zero polynomial. Solve for the zeros by finding which numbers make the statement true:
(x-8)(x-3)=0
(8-8)(8-3)= 0 * 5 = 0
(3-8)(3-3) = -5 * 0 = 0
x can equal 8 or 3
8^2 + 3^2 = 73 or
64 + 9 = 73
So one square will have a side with length 8ft and the other will have a side with length 3 ft.
2006-12-31 12:42:35 · answer #2 · answered by Rockstar 6 · 0⤊ 0⤋