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 [tex]s[/tex] be the length of the smaller square.
So, the length of the larger square = [tex]2s.[/tex]
Now, we find the areas of the square by putting formula:
The area of smaller square = length² [tex]=s^2.[/tex]
The area of larger square = (length)² [tex]=(2s)^2=4s^2.[/tex]
As, given:
The combined area of two squares is 80 square centimeters.
According to question:
[tex]s^2+4s^2=80\\5s^2=80[/tex]
So, dividing both sides by 5 we get:
[tex]s^2=16[/tex]
Using square root on both sides we get:
[tex]s=4\ centimeter.[/tex]
And, to get the length of each side of the larger square we substitute the value of [tex]s[/tex]:
[tex]2s=2\times 4=8\ centimeter.[/tex]
The length of larger square = 8 centimeter
Therefore, the length of each side of the larger square is 8 centimeter.
