Question

fill in the missing values to find the missing value of the triangle.
(right triangle with legs 6 in and 8 in, hypotenuse c)
$a^2 + b^2 = c^2$; $100 = c^2$
$8^2 + 6^2 = c^2$; $square = c$
$square + 36 = c^2$

Explanation:

Step1: Calculate \(8^2\)

We know that \(8^2 = 8\times8 = 64\). So the first missing value (in the left - hand side box) is \(64\) because we substitute \(a = 8\) into \(a^{2}\), and \(8^{2}=64\). The equation becomes \(64 + 36=c^{2}\).

Step2: Calculate \(c\) from \(100 = c^{2}\)

To find \(c\) when \(c^{2}=100\), we take the square root of both sides. Since \(c\) represents the length of a side of a triangle, we take the positive square root. \(\sqrt{100}=10\), so \(c = 10\).

Answer:

The first missing value (in the left box) is \(64\), and the second missing value (in the right box) is \(10\). So the completed equations are \(64+36 = c^{2}\) and \(10 = c\).