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

Question

The area of a rectangle is 256 cm².

One side is 4 times longer than the other.

What are the dimensions of the rectangle?

00:00 Find the rectangle's dimensions

00:04 Let's mark one side as length X

00:07 According to the given data, the second side is 4 times larger than the first side

00:10 Now let's use the formula for calculating rectangle area

00:13 Side(X) multiplied by side (4X)

00:16 Let's substitute appropriate values and 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 find the dimensions

00:35 Let's substitute in the side that's 4 times larger

00:41 And that's the solution to the problem

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:

$S=x\times4x$

$256=4x^2$

We divide the two sections by 4:

$64=x^2$

We extract the square root:

$x=\sqrt{64}=8$

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:

$8,8\times4=8,32$

8 x 32