Question

find the value of x.

1. surface area = 190 cm²

x =

Explanation:

Step1: Write the formula for the surface area of a rectangular prism

The formula for the surface area \(S\) of a rectangular prism is \(S = 2(lw+lh + wh)\), where \(l = 7\) cm, \(w = 2\) cm, \(h=x\) cm and \(S = 190\) \(cm^{2}\).
Substitute the values into the formula: \(190=2(7\times2 + 7x+2x)\)

Step2: Simplify the equation

First, simplify inside the parentheses: \(7\times2=14\), and \(7x + 2x=9x\).
The equation becomes \(190 = 2(14 + 9x)\).
Divide both sides by 2: \(\frac{190}{2}=\frac{2(14 + 9x)}{2}\), so \(95=14 + 9x\).

Step3: Solve for \(x\)

Subtract 14 from both sides: \(95-14=14 + 9x-14\), which gives \(81 = 9x\).
Divide both sides by 9: \(\frac{81}{9}=\frac{9x}{9}\), so \(x = 9\).

Answer:

\(x = 9\)