Asked by Tierra Walker on May 12, 2024
Verified
An open box with a rectangular base of x inches by x+4 inches has a height of 6 inches. The volume of the box is 702 cubic inches. Find the dimensions of the box.
A) 11 inches by 15 inches by 6 inches
B) 9 inches by 13 inches by 6 inches
C) 15 inches by 19 inches by 6 inches
D) 13 inches by 171717 inches by 6 inches
E) 131313 inches by 151515 inches by 6 inches
Rectangular Base
Refers to the base of a geometric figure that has a rectangle shape.
Cubic Inches
A unit of volume measurement in the Imperial system, specifically measuring space in three dimensions, symbolized as in³.
- Utilize quadratic equations in solving real-world issues, such as those found in geometry and optimization tasks.
Verified Answer
BE
brenna eberhartMay 12, 2024
Final Answer :
B
Explanation :
The volume of the box is given by $V=x(x+4)6=6x^2+24x=6(x^2+4x)$. Setting this equal to 702 and factoring, we have 6(x2+4x)=702x2+4x=117x2+4x−117=0(x+13)(x−9)=0\begin{align*}6(x^2+4x)&=702\\x^2+4x&=117\\x^2+4x-117&=0\\(x+13)(x-9)&=0\end{align*}6(x2+4x)x2+4xx2+4x−117(x+13)(x−9)=702=117=0=0 Since $x$ must be positive, we have $x=9$. Plugging this in, we get the dimensions of the box to be $9$ inches by $13$ inches by $6$ inches. Therefore, the answer is B.
Learning Objectives
- Utilize quadratic equations in solving real-world issues, such as those found in geometry and optimization tasks.