SOLUTION: the length of a rectangle is 3 m less than five times the width . the area of the rectangle is 36 m^2 find the dimensions

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Question 189435: the length of a rectangle is 3 m less than five times the width .
the area of the rectangle is 36 m^2 find the dimensions
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


We know for rectangle, Area = Length x Width

Given:
Width = x
Length = 5x-3, 3 meters less than 5 times width
Area = 36 sq m

Then,
36 = (5x-3)(x)
36 = 5x^2 - 3x
5x^2 - 3x -36 =0
Remember:system%28a=5%2Cb=%28-3%29%2Cc=%28-36%29%29
By Quadratic,
Discriminant: b%5E2-4ac=-3%5E2-4%285%29%28-36%29=9%2B720=red%28729%29
Then,
x=%28-%28-3%29%2B-sqrt%28729%29%29%2F%282%2A5%29=%283%2B-27%29%2F10
x=%283%2B27%29%2F10=30%2F10=red%283meters%29
x=%283-27%29%2F10=-24%2F10=-2.4, discard

So, Width=3 meters
Length = 5(3)-3 = 15-3 = 12 meters

Let's check,
A = L x W
36sq m = 12 x 3
36sq.m. = 36 sq. m.

Thank you,
Jojo