Question

45°
x
26√2

Explanation:

Step1: Identify the triangle type

This is a right - angled isosceles triangle (since one angle is \(45^{\circ}\), another is \(90^{\circ}\), so the third angle is \(45^{\circ}\)). 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 \(c\). Then \(c = a\sqrt{2}\).

Step2: Solve for \(x\)

Given \(c = 26\sqrt{2}\), and \(c=x\sqrt{2}\) (because in a \(45 - 45-90\) triangle, if the legs are \(x\) (equal in length for this type of right - triangle), hypotenuse \(c=x\sqrt{2}\)).
Set up the equation \(x\sqrt{2}=26\sqrt{2}\).
Divide both sides by \(\sqrt{2}\): \(x=\frac{26\sqrt{2}}{\sqrt{2}}\).

Answer:

\(x = 26\)