Question

f 18 m 18 m (right - angled at the bottom vertex)

Explanation:

Step1: Identify the triangle type

This is a right - isosceles triangle with legs \(a = b=18\space m\). To find the hypotenuse \(c\) (the side opposite the right angle, which is the base of the triangle here), we use the Pythagorean theorem. The Pythagorean theorem states that for a right triangle, \(c^{2}=a^{2}+b^{2}\).

Step2: Substitute the values

Substitute \(a = 18\) and \(b = 18\) into the formula:
\(c^{2}=18^{2}+18^{2}\)
\(c^{2}=324 + 324\)
\(c^{2}=648\)

Step3: Solve for \(c\)

Take the square root of both sides:
\(c=\sqrt{648}\)
Simplify \(\sqrt{648}=\sqrt{324\times2}=\sqrt{324}\times\sqrt{2}=18\sqrt{2}\approx18\times1.414 = 25.452\space m\) (if we want a decimal approximation) or we can leave it in exact form \(18\sqrt{2}\space m\).

If we want to find the area of the triangle, the formula for the area of a right triangle is \(A=\frac{1}{2}\times base\times height\). Here, base and height are both \(18\space m\).

Step4: Calculate the area (optional, if the question was about area)

\(A=\frac{1}{2}\times18\times18\)
\(A = 9\times18=162\space m^{2}\)

Since the problem was not clearly stated (whether to find the hypotenuse or the area), but based on the diagram, if we assume we need to find the hypotenuse (the length of the base \(F\)):

Answer:

If finding the hypotenuse (length of \(F\)): Exact form \(18\sqrt{2}\space m\approx25.45\space m\); If finding the area: \(162\space m^{2}\)