Question

The combined area of two squares is 80 square centimeters. Each side of one square is twice as long as a side of the other square. What is the length of each side of the larger square?

Answer 1

Answer:

The length of each side of the larger square is 8 centimeter.

Step-by-step explanation:

Given:

The combined area of two squares is 80 square centimeters. Each side of one square is twice as long as a side of the other square.

Now, to find the length of each side of the larger square.

Let $s$ be the length of the smaller square.

So, the length of the larger square = $2s.$

Now, we find the areas of the square by putting formula:

The area of smaller square = length²  $=s^2.$

The area of larger square = (length)²  $=(2s)^2=4s^2.$

As, given:

The combined area of two squares is 80 square centimeters.

According to question:

$s^2+4s^2=80\\5s^2=80$

So, dividing both sides by 5 we get:

$s^2=16$

Using square root on both sides we get:

$s=4\ centimeter.$

And, to get the  length of each side of the larger square we substitute the value of $s$:

$2s=2\times 4=8\ centimeter.$

The length of larger square = 8 centimeter

Therefore, the length of each side of the larger square is 8 centimeter.