Question

find u.
triangle with 45°, 45°, right angle, hypotenuse 20, side u
write your answer in simplest radical form.
blank units

Explanation:

Step1: Identify triangle type

The triangle is a right - isosceles triangle (two angles are \(45^{\circ}\), one right angle), so the two legs are equal, and the hypotenuse \(h\) and leg \(l\) satisfy \(h = l\sqrt{2}\). Here, hypotenuse \(h = 20\), leg is \(u\).

Step2: Solve for \(u\)

From \(h=l\sqrt{2}\), we can re - arrange to get \(l=\frac{h}{\sqrt{2}}\). Substitute \(h = 20\) into the formula: \(u=\frac{20}{\sqrt{2}}\). Rationalize the denominator by multiplying numerator and denominator by \(\sqrt{2}\): \(u=\frac{20\sqrt{2}}{\sqrt{2}\times\sqrt{2}}=\frac{20\sqrt{2}}{2}=10\sqrt{2}\).

Answer:

\(10\sqrt{2}\)