Question

a picture of a square floor tile is shown. the diagonal of the tile measures 12 inches. what is the area of the tile? a 36 in² b 72 in² c 144 in² d 288 in²

Explanation:

Step1: Recall Pythagorean theorem for square

Let side - length of square be $a$. In a square, if the diagonal is $d$, by Pythagorean theorem $d^{2}=a^{2}+a^{2}=2a^{2}$. Given $d = 12$ inches, so $12^{2}=2a^{2}$.

Step2: Solve for $a^{2}$

We have $144 = 2a^{2}$. Then $a^{2}=\frac{144}{2}=72$.

Step3: Find the area of the square

The area of a square $A=a^{2}$. Since $a^{2}=72$, the area of the square tile is $72$ square - inches.

Answer:

B. $72$ in$^{2}$