Consuelo's living room is in the shape of a rectangle and has an area of 360 square feet. The width of the living room is 5/8 its length. What is the length of the living room? HELPPPPPPP Please

Area of a rectangle is
A=lw

you have length which is 5/8 and the are which is 360.

so to find width you multiply the area by 8 and divide by 5

360= (5/8)(w)
2880=5w
576=w

you multiply by 8 because you're multiplying by the recipricol of 5/8

so w = 576 ft

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daftlydaft daftlydaft · Answer 2 · 2017-03-11T17:57:29+01:00

24 feet

Let length = x. because width is 5/8 the length, let width equal 5/8x.
Area equals length times width. Therefore, area equals:

[tex] \frac{5x}{8} [/tex] times "x" = [tex]360ft^{2} [/tex]

this equals [tex] \frac{5x^2}{8}[/tex] = [tex]360ft^{2} [/tex], because x times x is [tex] x^{2} [/tex]

Then multiply both sides by 8 to get rid of the fraction.

[tex]5 x^{2} [/tex] = [tex] 2880ft^{2} [/tex]

Divide both sides by 5 to get [tex] x^{2} [/tex] by itself.

[tex] x^{2} = 576ft^{2} [/tex]

Take the square of both sides to get x by itself.

[tex] \sqrt{x^2} = \sqrt{576ft^2} [/tex]

x = 24ft

You can check your answer by plugging in 24ft into your original equation.

[tex] \frac{5(24ft)}{8} [/tex] times (24ft) =[tex]360ft^{2} [/tex]

[tex] \frac{120ft}{8}[/tex] times 24 = [tex]360ft^{2} [/tex]

15ft times 24ft = [tex]360ft^{2} [/tex]

[tex]360ft^{2} [/tex] = [tex]360ft^{2} [/tex]