Q:

# the Gilberts are designing a rectangular patio for their backyard the patio has an area of 432 square feet the width of the patio 3/4 its length what is the length of the patio. please help

Accepted Solution

A:
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Given information
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Area = 432 ft²
Width = 3/4 of its length

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Form equation and solve for x
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Let the length be $$x$$
Therefore the width is $$\frac{3}{4} x$$

Area = Length x Widith
$$432 = x \times \frac{3}{4} x$$
$$432 =\frac{3}{4} x^2$$
[divide by 3/4 on both sides]
$$432 \div \frac{3}{4} =\frac{3}{4} x^2 \div \frac{3}{4}$$
$$576 = x^2$$
$$x^2 = 576$$
$$x = \sqrt{576}$$
$$x = 24$$

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Find Length
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Length = x = 24

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Answer : Length = 24 ft
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