MATH SOLVE

5 months ago

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 [tex]x[/tex]

Therefore the width is [tex] \frac{3}{4} x[/tex]

Area = Length x Widith

[tex]432 = x \times \frac{3}{4} x[/tex]

[tex]432 =\frac{3}{4} x^2[/tex]

[divide by 3/4 on both sides]

[tex]432 \div \frac{3}{4} =\frac{3}{4} x^2 \div \frac{3}{4} [/tex]

[tex]576 = x^2[/tex]

[tex]x^2 = 576[/tex]

[tex]x = \sqrt{576} [/tex]

[tex]x = 24[/tex]

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Find Length

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Length = x = 24

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Answer : Length = 24 ft

------------------------------------------------------------------

Given information

------------------------------------------------------------------

Area = 432 ft²

Width = 3/4 of its length

------------------------------------------------------------------

Form equation and solve for x

------------------------------------------------------------------

Let the length be [tex]x[/tex]

Therefore the width is [tex] \frac{3}{4} x[/tex]

Area = Length x Widith

[tex]432 = x \times \frac{3}{4} x[/tex]

[tex]432 =\frac{3}{4} x^2[/tex]

[divide by 3/4 on both sides]

[tex]432 \div \frac{3}{4} =\frac{3}{4} x^2 \div \frac{3}{4} [/tex]

[tex]576 = x^2[/tex]

[tex]x^2 = 576[/tex]

[tex]x = \sqrt{576} [/tex]

[tex]x = 24[/tex]

------------------------------------------------------------------

Find Length

------------------------------------------------------------------

Length = x = 24

------------------------------------------------------------------

Answer : Length = 24 ft

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