Question

find t. 10\sqrt{2} mm write your answer in simplest radical form. millimeters

Explanation:

Step1: Identify the triangle type

This is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the ratio of the sides is \(1:1:\sqrt{2}\). Let the legs be of length \(a\) and the hypotenuse be \(c\). The formula is \(c = a\sqrt{2}\).

Step2: Solve for \(t\)

Given the hypotenuse \(c=10\sqrt{2}\) mm. Using \(c = a\sqrt{2}\), substitute \(c\):

$$10\sqrt{2}=t\sqrt{2}$$

Divide both sides by \(\sqrt{2}\):

$$t=\frac{10\sqrt{2}}{\sqrt{2}} = 10$$

Answer:

\(10\)