Question

Constructed Response

Two skyscrapers are under construction in Atlanta. They will sit on opposite sides of Peachtree St. and
the architect has designed them to be similar. The architect made a sketch of two rectangles to model
the front view of the two buildings and included the following statement: ABCD ~ JKLM. It was also given
that AB = 1600 ft., BC = 200 ft., and JM = 150 ft.. Use the scenario to solve problems (a) through (d)

a.) Which rectangle is being used to model the taller building?

b.) Which line segments could be used to model the height of the smaller building?

c.) What is the height of the taller building? Explain your reasoning.

d.) What is the height of the smaller building? Explain your reasoning.

e.) Would it make sense to say that the scale factor from smaller building to taller building is 3/4?
Explain your reasoning.

Answer 1

A rectangle is a quadrilateral which has the length of its opposite sides to be equal. Thus, the following are the solutions to the questions:

a) The rectangle used to model the taller building is ABCD.

b) The line segment used to model the height of the smaller building is JM = KL.

c) The height of the taller building is 200 feet.

d) The height of the smaller building is 150 feet.

e) Yes, the scale factor from small to tall building is $\frac{3}{4}$.

Rectangles have equal length of opposite sides , and the sum of its interior angles to be $360^{o}$. Since the two given skyscrapers were modeled with respect to rectangles ABCD and JKLM, then the answers to the questions are:

a) The rectangle used to model the taller building is ABCD. Since the length of a rectangle is always greater than its width. So that the height; AD = BC.

b) The line segment that can be used to model the height of the smaller building is; JM = KL. This represent the width of the rectangular model for the small building.

c) The height of the taller building is AD = BC = 200 feet. The width of a rectangle is often smaller than its length, which in this case is the height.

d) The height of the smaller building is JM = KL = 150 feet. The length of a rectangle is usually longer than its width.

e) Yes, it would make sense because:

scale factor = $\frac{height of the smaller building}{height of the taller building}$

                   = $\frac{150 ft}{200ft}$

                   = $\frac{15}{20}$

scale factor = $\frac{3}{4}$

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