Question

NO LINKS!!

Shown in the figure is a cross-section of a design for a two-story home. The center height h of the second story has not yet been determined. Find h such that the second story will have the same cross-sectional area as the first story.

h = __________ ft

Answer 1

h = 13 ft

Explanation:

The cross-sectional area of the first story is the area of a rectangle with width 30 ft and height 8 ft. The area of a rectangle is the product of its width and height.

`\begin{aligned}\implies \textsf{Cross-sectional area of first story}&=30 * 8\\&=240\; \sf ft^2\end{aligned}`

The cross-sectional area of the second story is made up of a rectangle with width 30 ft and height 3 ft, and a triangle with base 30 ft and height (h - 3). The area of a triangle is half the product of its base and height.

`\begin{aligned}\implies \textsf{Cross-sectional area of second story}&=(30 * 3)+(1)/(2) * 30 * (h-3)\\&=90+15(h-3)\\&=90+15h-45\\&=(15h+45)\; \sf ft^2\end{aligned}`

If the second story has the same cross-sectional area as the first story, then:

`\implies 15h+45=240`

To find h, solve the equation:

`\begin{aligned}\implies 15h+45&=240\\15h&=195\\h&=13\; \sf ft\end{aligned}`

Therefore, the value of h such that the second story will have the same cross-sectional area as the first story is 13 ft.