Question

determine the length of the hypotenuse for the given 45 - 45 triangle: 4√5 8√5 8√10 8√3

Explanation:

Step1: Recall the property of a 45 - 45 - 90 triangle

In a 45 - 45 - 90 triangle, the legs are equal. Let the length of each leg be \(a\). The formula for the hypotenuse \(c\) is \(c = a\sqrt{2}\).

Step2: Find the length of the leg

From the figure (assuming the leg length is \(4\sqrt{10}\) (since if we consider the non - hypotenuse side of the right - angled triangle formed, and using the property of the rectangle (opposite sides are equal)). Wait, no, let's assume the leg length \(a = 4\sqrt{5}\times2=8\sqrt{5}\) (if we consider the non - hypotenuse side of the right - angled triangle. Another way: using the Pythagorean theorem \(c^{2}=a^{2}+a^{2}\) (since \(a = b\) in 45 - 45 - 90 triangle). If \(a = 8\sqrt{5}\), then \(c^{2}=(8\sqrt{5})^{2}+(8\sqrt{5})^{2}\).

$$
LATEXBLOCK0
$$

Answer:

\(8\sqrt{10}\)