Question

instructions
choose the best answer. if necessary, use the paper you were given.
question
the edges of a rectangular solid have lengths ( 2x ), ( 3x ), and ( 5x ). what is the total surface area of the solid?
( 30x^{2} )
( 60x^{2} )
( 62x^{2} )
( 30x^{3} )

Explanation:

Step1: Recall the formula for the surface area of a rectangular solid

The formula for the surface area \(S\) of a rectangular solid with length \(l\), width \(w\), and height \(h\) is \(S = 2(lw+lh + wh)\). Here, \(l = 2x\), \(w=3x\), and \(h = 5x\).

Step2: Calculate \(lw\), \(lh\), and \(wh\)

• \(lw=(2x)(3x)=6x^{2}\)
• \(lh=(2x)(5x) = 10x^{2}\)
• \(wh=(3x)(5x)=15x^{2}\)

Step3: Substitute into the surface - area formula

\(S=2(6x^{2}+10x^{2}+15x^{2})\). First, simplify the sum inside the parentheses: \(6x^{2}+10x^{2}+15x^{2}=(6 + 10+15)x^{2}=31x^{2}\). Then, \(S = 2\times31x^{2}\).

Answer:

\(62x^{2}\)