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Galina-37 [17]
3 years ago
11

Area = 300 square feet

Mathematics
1 answer:
m_a_m_a [10]3 years ago
3 0

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

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