Question

find a and b. a = 10√2, b = 10√2 a = 5√2, b = 5√2 a = 10, b = 10√2 a = 5, b = 5

Explanation:

Step1: Identify the triangle type

This is a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle. In a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle, the legs are equal (\(a = b\)), and the hypotenuse \(c\) is related to the leg \(x\) by the formula \(c=x\sqrt{2}\).

Step2: Solve for \(a\) and \(b\)

Given the hypotenuse \(c = 10\). Let \(a=b=x\). Using \(c=x\sqrt{2}\), we substitute \(c = 10\) into the formula: \(10=x\sqrt{2}\). Solving for \(x\) (which is \(a\) and \(b\)), we get \(x=\frac{10}{\sqrt{2}}=\frac{10\sqrt{2}}{2}=5\sqrt{2}\).

Answer:

\(a = 5\sqrt{2}, b = 5\sqrt{2}\)