Question

pre-algebra ic sem 2 fall 2025
square roots and right triangles
what is the length of the unknown leg in the right triangle?

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here \(b = 21\) cm and \(c=29\) cm. We need to find \(a\). So, \(a^{2}=c^{2}-b^{2}\).

Step2: Substitute values

\(a^{2}=29^{2}-21^{2}\).
Using the formula \((x + y)(x - y)=x^{2}-y^{2}\), \(29^{2}-21^{2}=(29 + 21)(29 - 21)\).
\(29+21 = 50\) and \(29 - 21=8\). So, \(a^{2}=50\times8=400\).

Step3: Find \(a\)

Take the square root of \(a^{2}\). \(a=\sqrt{400}\). Since \(20\times20 = 400\), \(a = 20\) cm.

Answer:

20 cm