Question

a rectangular prism has a surface area of 728 square centimeters and a height of 4 centimeters. its base has a width of 15 centimeters. what is the length of the base of the prism? centimeters submit

Explanation:

Step1: Recall the surface area formula

The surface area formula of a rectangular prism is \(S = 2(lw+lh + wh)\), where \(l\) is length, \(w\) is width, and \(h\) is height. Given \(S = 728\), \(w = 15\), \(h=4\).

Step2: Substitute the values into the formula

Substitute into \(728=2(l\times15 + l\times4+15\times4)\). First, simplify the equation: divide both sides by 2. We get \(364=15l + 4l+60\).

Step3: Combine like - terms

Combine \(15l\) and \(4l\). So \(364 = 19l+60\).

Step4: Solve for \(l\)

Subtract 60 from both sides: \(364 - 60=19l\), which gives \(304 = 19l\). Then divide both sides by 19: \(l=\frac{304}{19}\).

Answer:

\(16\)