The volume of a rectangular prism is 1,560 cm3. The height is 12 cm. The width is w and the length is w + 3. Find w.

Answers

Answer 1

Volume = w * h * l
w = w, h = 12, l = w + 3
1,560 = w * 12 * w + 3
1,560 = 12w^2 + 3
-12w^2 = 3 - 1,560
-12w^2 = -1557
w^2 = 519/4
w = 11.39079 cm
You can round it if you want

Answer 2

Answer:

w=10 cm

Step-by-step explanation:

The formula for the volume of a rectangular prism is V=whl.

So in this case, the equation would be 1560=w·12·(w+3). Then, we can simplify this equation.

1. Divide 12 to both sides of the equation. 1560/12=130. The equation becomes 130=w(w+3).

2. Distribute w through the parentheses, the equation becomes 130=w²+3w.

3. Then, -130 from both sides of the equation, so we can get the quadratic: w²+3w-130=0.

4. Factor the quadratic. w²+3w-130=(w-10)(w+13).

5. (w-10)(w+13)=0. w=10 or w=-13. However, w is the width of a rectangular prism, can the width of a shape be negative? No. So we can ignore the solution w=-13. Therefore, w=10cm.

6. To make sure our answer is correct, let's substitute the values back into the volume of a rectangular prism formula: V=whl. w=10; h=12; l=10+3=13; V=10(12)(13)=120*13=1560 cm³. As a result, our answer is correct, w=10 cm.

Hope this helps, have a nice day.

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