Question

1. find the missing dimension, given the surface area of the 3 - d object and the diagram. round to the nearest whole number.

a. sa = 78 ft²
we know
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Explanation:

Step1: Recall surface - area formula

The surface - area formula for a rectangular prism is $SA = 2(lw+lh + wh)$, where $l = 5$ ft, $h = 3$ ft, and $w$ is the unknown dimension, and $SA=78$ ft². Substitute the known values into the formula: $78=2(5w + 5\times3+3w)$.

Step2: Simplify the equation

First, simplify the expression inside the parentheses: $78 = 2(5w+15 + 3w)=2(8w + 15)$. Then, distribute the 2: $78=16w+30$.

Step3: Solve for $w$

Subtract 30 from both sides of the equation: $78 - 30=16w$, so $48 = 16w$. Divide both sides by 16: $w=\frac{48}{16}=3$ ft.

Answer:

$3$ ft