A rectangle has an area of 115 square yards. The width is 3 more than 4 times the length. Find the length and width, in yards, of the rectangle.

Answer 1

Area of a rectangle = Length * Width

Area = 115yds²

width= 4L+3

115=(4L+3)*L

115= 4L^2+3L

4L^2+3L-115=0

 

Use the quadratic formula to solve for L

-b ±√ b² - 4 (a)(c)

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       2a

L= 5 or -23/4 but you can't have a negative value for a side. That leaves L as 5 yards

 

 

 

L=5

w=4L+3

W=3+4(5)

W=23

 

so the dimensions are 23 for the width and 5 as the length. A sanity check with 5*23=115 which was what our area equals checks out.