Question

b
a
36m
x
c
18m
d

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle \(BCD\) (since \(ABCD\) is a rectangle, \(\angle C = 90^{\circ}\)), the Pythagorean theorem states that for a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here, \(a = 36\) and \(b = 18\), and \(x\) is the hypotenuse. So, \(x^{2}=36^{2}+18^{2}\).

Step2: Calculate \(36^{2}\) and \(18^{2}\)

\(36^{2}=(30 + 6)^{2}=30^{2}+2\times30\times6+6^{2}=900+360 + 36=1296\).
\(18^{2}=(20 - 2)^{2}=20^{2}-2\times20\times2+2^{2}=400-80 + 4=324\).
Then \(x^{2}=1296+324\).

Step3: Sum the values

\(x^{2}=1296 + 324=1620\).

Step4: Simplify \(\sqrt{x^{2}}\)

\(x=\sqrt{1620}=\sqrt{324\times5}\). Since \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a = 324\), \(b = 5\)), and \(\sqrt{324}=18\), so \(x = 18\sqrt{5}\approx18\times2.24 = 40.32\) (using \(\sqrt{5}\approx2.24\)).

Answer:

\(x = 18\sqrt{5}\text{ m}\approx40.32\text{ m}\)