Consuelos living room is in the shape of a rectangle and has an area of 360 square feet. The width of the living room is 5/6 it's length. What is the length of living room?

W = 5/6 L

A = L times W

A = l times 5/6 L

360 = 5/6 times L squared

360 times 6/5 = L squared

Multiply 360 times 6 divide that answer by 5. Now take the square root to find L.

Let's denote the length of the living room as L.

According to the given information, the width of the living room is 5/6 times its length.

Therefore, the width of the living room can be expressed as:
Width = (5/6)L

We also know that the area of a rectangle is equal to its length multiplied by its width. In this case, the area of the living room is 360 square feet.

So we can write the equation:
Area = Length * Width

Substituting the values we calculated, we have:
360 = L * (5/6)L

To simplify further, we can multiply the fractions:
360 = (5L/6) * L

Now, let's solve for L by multiplying both sides of the equation by 6/5 (reciprocal of 5/6):
(6/5) * 360 = (6/5) * (5L/6) * L

Simplifying the equation:
432 = L^2

Taking the square root of both sides, we have:
L = √432

L ≈ 20.7846

Therefore, the length of the living room is approximately 20.7846 feet.

To find the length of the living room, we can start by setting up an equation based on the given information.

Let's assume the length of the living room is "L" and the width is "W." We are given that the area of the living room is 360 square feet, so we can write the equation:

Area = Length × Width

360 = L × W

The problem also states that the width of the living room is 5/6 of its length. So, we can substitute "5/6 L" for "W" in the equation:

360 = L × (5/6 L)

To simplify, we multiply the length terms:

360 = (5/6) L²

To get rid of the fraction, we can multiply both sides of the equation by 6:

(6 × 360) = 5 × L²

2160 = 5 × L²

To isolate L², we divide both sides of the equation by 5:

2160/5 = L²

432 = L²

Now, we can take the square root of both sides to find the length:

√432 = √L²

L ≈ 20.78 (rounded to two decimal places)

Hence, the length of the living room is approximately 20.78 feet.

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