Question

1. surface area = 202 m²

x
13 m
x =

Explanation:

Step1: Recall the surface area formula for a rectangular prism

The surface area formula for a rectangular prism is \(SA = 2(lw+lh + wh)\), where \(l = 13\)m, \(w=x\)m, \(h = 5\)m, and \(SA=202\)m². Substitute the values into the formula: \(202=2(13x + 13\times5+5x)\).

Step2: Simplify the equation

First, divide both sides of the equation by 2: \(\frac{202}{2}=\frac{2(13x + 65+5x)}{2}\), which gives \(101=13x+65 + 5x\). Then combine like - terms: \(101=(13x + 5x)+65\), so \(101 = 18x+65\).

Step3: Solve for \(x\)

Subtract 65 from both sides: \(101 - 65=18x+65 - 65\), which results in \(36 = 18x\). Then divide both sides by 18: \(\frac{36}{18}=\frac{18x}{18}\).

Answer:

\(x = 2\)