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