Question

Several years ago, Matt built a rectangular flower bed at his house. The width of the flower bed was 14 inches less than the length of the flower bed. This spring, Matt decides to build a new rectangular flower bed at his house that covers the same area as the old flower bed. After some planning, he decides that the length of the new flower bed should be 8 inches less than the width of the old flower bed, and that the width of the new flower bed should 8 inches greater than two times the length of the old flower bed.
What is the approximate length of the old flower bed?
A. 28.23 inches
B. 16.37 inches
C. 6.23 inches
D. 24.47 inches

Answer 1

Answer:

A. 28.23 inches

Step-by-step explanation:

Since the are of the old and new flower bed are the same,

                $A_{old}$ = $A_{new}$

 l(l- 14) = (l- 22)(2l+ 8)

$l^{2}$- 14l = 2$l^{2}$ +8l -44l -176

$l^{2}$- 14l = 2$l^{2}$ -36l -176

combining the terms to form a quadratic equation;

$l^{2}$ - 2$l^{2}$ -14l +36l +176 = 0

-$l^{2}$ +22l + 176 = 0

multiply through by minus sign;

$l^{2}$ -22l - 176 = 0

Applying the quadratic formula,

    $\frac{-b }{2}$ ± $\sqrt{b^{2} - 4ac }$

a = 1, b= -22 and c = -176

substitute these values in the equation,

=  $\frac{22}{2}$ ±$\sqrt{484 + 704}$

= 28.233688

= 28.23 inches

Answer 2

D. 24.47 inches
I think this is the right answer