Question

fill in the missing values to find the missing value of the triangle.
(right triangle with legs 12 in and 9 in, hypotenuse c)
$a^2 + b^2 = c^2$
$12^2 + 9^2 = c^2$
$\square + 81 = c^2$
$225 = c^2$
$\square = c$

Explanation:

Step1: Calculate \(12^2\)

We know that \(12^2 = 12\times12 = 144\). So the first missing value (in the left - hand side box) is \(144\) because we substitute \(a = 12\) into \(a^{2}\), and \(12^{2}=144\). Then the equation becomes \(144 + 81=c^{2}\), and \(144 + 81=225\), so \(c^{2}=225\).

Step2: Solve for \(c\)

To find \(c\) when \(c^{2}=225\), we take the square root of both sides. Since \(c\) represents the length of a side of a triangle (the hypotenuse), we take the positive square root. We know that \(\sqrt{225}=15\) because \(15\times15 = 225\). So the second missing value (in the right - hand side box) is \(15\).

Answer:

The left - hand side box (under \(12^{2}\)) is \(144\), and the right - hand side box (for \(c\)) is \(15\). If we consider the final value of \(c\) (the question might be asking for the value of \(c\) or the missing values in the boxes), the value of \(c\) is \(15\) and the value of \(12^{2}\) is \(144\). If we focus on the value of \(c\), the answer is \(15\).