a rectangle with are 315 square inches has a length that is one less than four times the width. find the length and the width of the rectangle

l=35 inches

w = 9 inches

Step-by-step explanation:

Area is 315 square inches

Area=l*w=315 (Equation 1)

l=4w-1 (Equation 2)

Putting value of l from equation 2 in equation 1

(4w-1) w=315

4w^2-w-315=0

Solving by using quadratic equation

a=4, b=-1, c=-315

w = (-b+sqrt (b^2-4ac)) / 2a and w = (-b-sqrt (b^2-4ac)) / 2a

w = (1+sqrt (1+5040)) / 8 and w = (1-sqrt (1+5040)) / 8

w = (1+sqrt (5041)) / 8 and w = (1-sqrt (5041)) / 8

sqrt (5041) = 71

w = (1+71) / 8 and w = (1-71) / 8

w=72/8 and w=-70/8

as width can't be a negative number so we'll solve for w=72/8=9

width = 9 inches

putting w in equation 2

l = (4*9) - 1

l=35 inches