Question

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Answer 1

The length of side of largest square is 15 inches

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

`s^2 = A\\s^2 = 81\\√(s^2) = √(81)\\s = 9`

Perimeter of square 2: 48 inches

`4*side = P\\4* side = 48\\side = (48)/(4)\\side = 12\ inches`

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.

`(H)^2 = (P)^2+(B)^2\\H^2 = (9)^2+(12)^2\\H^2 = 81+144\\H^2 = 225\\√(H^2) = √(225)\\H = 15`

Hence,

The length of side of largest square is 15 inches