Question

lesson 7: triangles
pythagorean theorem
which of the following is the length of the missing side
in the illustration to the right?

a. 16 cm
b. 4 cm
c. 3 cm
d. 4.3 cm
check answer

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with hypotenuse \(c\) and legs \(a\) and \(b\), \(c^{2}=a^{2}+b^{2}\). Here, the hypotenuse \(c = 5\space cm\) and one leg \(b=3\space cm\), and we need to find the other leg \(a\). Rearranging the formula for \(a\), we get \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute the values

Substitute \(c = 5\) and \(b = 3\) into the formula: \(a=\sqrt{5^{2}-3^{2}}=\sqrt{25 - 9}=\sqrt{16}\)

Step3: Calculate the square root

\(\sqrt{16}=4\space cm\)

Answer:

b. 4 cm