Answer:
The length of side of largest square is 15 inches
Step-by-step explanation:
The given suares are when joined in the way as shown in picture their sides form a right agnled triangle.
Area of square 1 and perimeter of square 2 will be used to calculate the sides of the triangle.
So,
Area of square 1: 81 square inches
[tex]s^2 = A\\s^2 = 81\\\sqrt{s^2} = \sqrt{81}\\s = 9[/tex]
Perimeter of square 2: 48 inches
[tex]4*side = P\\4* side = 48\\side = \frac{48}{4}\\side = 12\ inches[/tex]
We can see that a right angled triangle is formed.
Here
Base = 12 inches
Perpendicular = 9 inches
And the side of largest square will be hypotenuse.
Pythagoras theorem can be used to find the length.
[tex](H)^2 = (P)^2+(B)^2\\H^2 = (9)^2+(12)^2\\H^2 = 81+144\\H^2 = 225\\\sqrt{H^2} = \sqrt{225}\\H = 15[/tex]
Hence,
The length of side of largest square is 15 inches
