A landscaper, who just completed a rectangular flower garden measuring 15 feet in length by 6 feet in width, orders 1 cubic yard of premixed cement, all of which is to be used to create a border of uniform width around the garden. If the border is to have a depth of 2 inches, how wide will the border be? left parenthesis 1 cubic yard equals 27 cubic feet right parenthesis

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calculista calculista · Answer 1 · 2019-08-25T16:46:40+02:00

Answer:

The uniform width around the garden is 3 ft

Step-by-step explanation:

Remember that

1 yd=3 ft

1 ft=12 in

1 yd³=27 ft³

step 1

Convert cubic yards to cubic feet

The volume of premixed cement is 27 ft³

step 2

Find the uniform width around the garden

Let

x ------> the uniform width around the garden

we know that

The area of the border is equal to

[tex]A=[(15+2x)(6+2x)-((15)(6)]\\A=90+30x+12x+4x^{2}-90\\A=4x^{2}+42x[/tex]

To Find the volume , multiply the area by the depth

The depth is 2 inches

Convert to ft

2 in=2/12=1/6 ft

The volume is equal to

[tex]V=[4x^{2}+42x](1/6)\\ \\V=\frac{2}{3}x^{2}+7x[/tex]

Remember that

[tex]V=27\ ft^{3}[/tex]

Equate the volumes

[tex]\frac{2}{3}x^{2}+7x=27[/tex]

[tex]\frac{2}{3}x^{2}+7x-27=0[/tex]

using a graphing tool solve the polynomial

The solution is x=3 ft

see the attached figure