Question

The perimeters of two squaresin the model are given.Find the perimeter ofthe third square.P =12 unitsP=16 units02

Answer 1

Given the diagram represents 3 squares constructed by the sides of a right-angle triangle.

The model is used to prove the Pythagorean theorem.

The square with a perimeter of 12 units, has a side length = 3 units

And the square with a perimeter of 16 units has a side length = 4 units

Using the Pythagorean theorem to find the length of the third square

Where is the side of the third square is the hypotenuse of the triangle

So, let the side of the third square = h

`\begin{gathered} h^2=3^2+4^2=25 \\ h=√(25)=5 \end{gathered}`

The perimeter of the square is 4 times the side length

so, the perimeter od the third square = 4 * 5 = 20 units

So, the answer will be:

The perimeter of the third square = 20 units