Question

4.7 understand: introduction to the pythagorean theorem
show what you know
if a right triangle has legs measuring 6 and 8, what is the length of the hypotenuse?
10
14
15
12

Explanation:

Step1: Apply Pythagorean Theorem

The Pythagorean Theorem is \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs of a right - triangle and \(c\) is the hypotenuse. Given \(a = 6\) and \(b=8\), we substitute these values into the formula: \(6^{2}+8^{2}=c^{2}\).

Step2: Calculate squares

\(6^{2}=36\) and \(8^{2}=64\). So the equation becomes \(36 + 64=c^{2}\).

Step3: Sum the values

\(36+64 = 100\), so \(c^{2}=100\).

Step4: Solve for \(c\)

Take the square root of both sides. Since \(c>0\) (length cannot be negative), \(c=\sqrt{100}=10\).

Answer:

10