Find Rectangle Dimensions: Area 256 cm² with 4:1 Side Ratio

The area of a rectangle is 256 cm².

One side is 4 times longer than the other.

What are the dimensions of the rectangle?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine the rectangle's dimensions
00:04 Mark one side as the length X
00:07 According to the given data, the second side is 4 times larger than the first side
00:10 Apply the formula for calculating the area of a rectangle
00:13 Side(X) x side (4X)
00:16 Substitute in the relevant values and proceed to solve for X
00:24 Take the square root
00:29 That's the value of X, now let's substitute in the rectangle's sides to determine the dimensions
00:35 Substitute in the side that's 4 times larger
00:41 That's the solution

Step-by-step written solution

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1

Understand the problem

The area of a rectangle is 256 cm².

One side is 4 times longer than the other.

What are the dimensions of the rectangle?

2

Step-by-step solution

To find the area of the rectangle, we multiply the length by the width.

According to the data in the statement, one side will be equal to X and the other side will be equal to 4X

Now we replace the existing data:

S=x×4x S=x\times4x

256=4x2 256=4x^2

We divide the two sections by 4:

64=x2 64=x^2

We extract the square root:

x=64=8 x=\sqrt{64}=8

If we said that one side is equal to x and the other side is equal to 4x and we know that x=8

From here we can conclude that the sides of the rectangle are equal:

8,8×4=8,32 8,8\times4=8,32

3

Final Answer

8 x 32

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle ABCD below.

Side AB is 6 cm long and side BC is 4 cm long.

What is the area of the rectangle?
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