Question

a rectangular box has two sides whose lengths are 3 centimeters and 5 centimeters and a volume of 135 cm³. what is the area of its largest side?

1. 17 cm²
2. 36 cm²
3. 29 cm²
4. 45 cm²

Explanation:

Step1: Find the third - side length

Let the side lengths be $a = 3$ cm, $b = 5$ cm, and the volume $V=135$ cm³. Using the volume formula for a rectangular box $V=a\times b\times c$, we can find $c$. So $c=\frac{V}{a\times b}$. Substituting the values, we have $c=\frac{135}{3\times5}=\frac{135}{15} = 9$ cm.

Step2: Calculate the areas of different sides

The areas of the three pairs of sides are: $A_1=a\times b=3\times5 = 15$ cm², $A_2=a\times c=3\times9 = 27$ cm², $A_3=b\times c=5\times9 = 45$ cm².

Answer:

45 cm²