Question

Area = 300 square feet

Answer 1

Answer:

$Length=24.32$ feet

$width=12.32$ feet

Step-by-step explanation:

Let x be the width of a rectangle

Let l be the length of a rectangle

Let A be the area of rectangle

Given.

Length must be 12 feet longer than width

therefore

$Length=12+w$

$l=12+w$

Area of rectangle

$A=300$

We know that area of rectangle is

$A=l\times w$---------------------(1)

put all known values in equation 1

$300=(12+x)\times x$

$x^{2} +12x=300\\x^{2} +12x-300=0$

Find roots by this formula

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

$=\frac{-12\pm\sqrt{12^{2}-4(1)(-300)}}{2(1)}$

$=\frac{-12\pm\sqrt{1344}}{2}$

$x=-6+4\sqrt{21} \\x=-6-4\sqrt{21}$

$x=12.32\\x=-24.32$

check both value in equation 1

for $x=12.32$

$A=(12+12.32)\times 12.32$

$A=299.62$

$x=12.32$ is satisfy the equation

So The length of rectangle $l=12+12.32$=24.32 feet

And width is 12.32 feet