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A rectangular dining room has an area of 20 square meters. It's perimeter is 18 meters. What are the dimensions of the dining room?

User Gus
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2 Answers

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Final answer:

To find the dimensions of the rectangular dining room, we can use the given information about the area and perimeter. Using the equations for area and perimeter, we can solve a system of equations to find the values of length and width. The dimensions of the dining room are 4 meters by 5 meters.

Step-by-step explanation:

To find the dimensions of the rectangular dining room, we need to use the given information.

Let's assume the length of the dining room is x meters and the width is y meters.

According to the given information, the area is 20 square meters, so we have the equation:

x * y = 20

Since the perimeter is 18 meters, we have another equation:

2x + 2y = 18

Now, we can solve the system of equations to find the values of x and y:

2x + 40/x = 18.

2x^2 + 40 = 18x. Rearrange to form a quadratic equation:

2x^2 - 18x + 40 = 0.

Factor the quadratic equation or use the quadratic formula to find the solutions for x:

x = 4 or x = 5.

Now, substitute these values of x back into the equation y = 20/x to find the corresponding values for y:

When x = 4, y = 20/4 = 5.

When x = 5, y = 20/5 = 4.

Therefore, the dimensions of the dining room are 4 meters by 5 meters.

User InspectorSands
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8.5k points
12 votes

Answer:

The dimensions are:

Length = 5m and Width = 4m

Or

Length = 4m and Width = 5m

Step-by-step explanation:

A rectangular dining room has an area of 20 square meters. It's perimeter is 18 meters. What are the dimensions of the dining room?

Area of a rectangle = Length × Width

= LW = 20 m²

Perimeter of a rectangle =

2L + 2W = 18 m

Hence:

LW = 20...... Equation 1

L = 20/W

2L + 2W = 18 ...... Equation 2

We substitute

20/W for L in Equation 2

2(20/W) + 2W = 18

40/W + 2W = 18

Multiply through by W

40 + 2W² = 18W

2W² - 18W + 40 = 0

2W² - 10W - 8W + 40 = 0

(2W - 8 )(W - 5) = 0

2W - 8 = 0

2W = 8 , W = 8/2 = 4m

W - 5 = 0

W = 5m

W = 4m or 5 m

Solving for L

When W = 5 m

L = 20/W

L = 20/5

L = 4m

When W = 4m

L = 20/W

L = 20/4

L = 5m

Therefore, the dimensions are:

Length = 5m and Width = 4m

Or

Length = 4m and Width = 5m

User Truth
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