Question

The length of a rectangular floor is 7 feet longer than its width w. The area of the floor is 505 ft2

Answer 1

Answer:

Width is 19.24 ft and length is 24.24 ft

Step-by-step explanation:

Step 1:  Write an equation

$A = l * w$

$505\ ft^2 = (7+w) * w$

$505\ ft^2 = (w*w) + (w*7)$

$505\ ft^2 - 505\ ft^2 = w^2 + 7w - 505\ ft^2$

$0= w^2 + 7w - 505\ ft^2$

Step 2:  Determine the dimensions

Use Quadratic formula

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-7\pm\sqrt{(7)^2-4(1)(-505)}}{2(1)}$

$x=\frac{-7\pm\sqrt{2069}}{2}$

$x = \frac{-7\pm45.486}{2}$

$x=19.24,\ -26.24$

Since length cannot be negative, we will use 19.24 for x.

Step 3:  Determine the length

$l = w + 5$

$l = 19.24 + 5$

$l = 24.24$

Answer:  Width is 19.24 ft and length is 24.24 ft