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a rectangular field has a perimeter of 500m and an area of 14400m2.  Find the lengths of the sides

Sagot :

anniedavies96
perimeter = 500 = 2x + 2y, where x and y are the length and width

area = 14400 = xy
x = 14400 / y

substitute:
500 = (2* (14400/y)) + 2y
[multiply by y]
500y = 28800 + 2y^2
2y^2 - 500y + 28800 = 0
y^2 - 250y + 14400 = 0

use the quadratic equation: y = (-b ± (b^2 - 4*a*c)^1/2) / 2a
the answers should be written in the form (y - answer one) (y- answer two)

substitute these answers into x = 14400 / y to find x
remember x and y  can not be negative as they are lengths
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