Question

Which of the following could be the areas of the three squares below? A. 12ft^2, 16ft^2, 20ft^2B. 10ft^2, 18ft^2, 30ft^2C. 4ft^2, 5ft^2, 12ft^2D. 8ft^2, 16ft^2, 24ft^2i have to show work too :(

Answer 1

Answer:

The correct option is D

8ft^2, 16ft^2, 24ft^2 could be the three areas of the given squares

Step-by-step explanation:

To know the area of the three squares, we need to know the side length of each square. This can be done by applying Pythagorean rule on the right-angle triangle formed in the middle.

The square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides (legs).

The area of a square is the square of its side length.

Taking the square roots of each of the given options, which ever option has Pythagorean triple is the correct option.

A.

`2\sqrt[]{3},4,2\sqrt[]{5}`

This is NOT a Pythagorean triple.

B.

`\sqrt[]{10},3\sqrt[]{2},\sqrt[]{30}`

This is NOT a Pythagorean triple.

C.

`2,\sqrt[]{5},2\sqrt[]{3}`

This is NOT a Pythagorean triple

D.

`2\sqrt[]{2},4,2\sqrt[]{6}`

This is a Pythagorean triple.

CHECK

`\begin{gathered} (2\sqrt[]{2})^2+4^2=(2\sqrt[]{6})^2 \\ 8+16=24 \\ 24=24 \end{gathered}`