Question

12 if quadrilateral q is a scaled copy of quadrilateral p (diagram of trapezoid p with sides 15, 15, 25, top side i)
13 marcus drew a scale drawing of the rectangular park in his neighborhood. on his drawing, the length of the park is 8 inches and the width of the park is 6 inches. the key on his drawing shows 1 inch = 20 feet. what is the actual area of the park?
a 360 square feet
b 960 square feet
c 5,000 square feet
d 19,200 square feet
14 a building has a height of 125 meters and a length of 80 meters. on a scale drawing of the building, the height is 25 meters. what is the length of the building on the scale drawing in meters?
a 55 m
b 16 m
c 20 m
d 64 m
15 what is the length of y if the scale factor is 2? (diagram of triangles abc and def, abc with sides 5 cm, 6 cm, 8 cm; def with side 10 cm, y, x)
options: 6 cm, 10 cm, 12 cm, 3 cm
sam drew △abc, then applied a scale factor of 2 1/3 to draw △qrs. (diagram of △abc with sides 9, 12, 15; △qrs with some sides marked? what are the side lengths for △qrs? select the box in each row to identify the correct value for each side. options: 11 1/3, 14 1/3, 17 1/3, 21, 28)

Explanation:

Question 13 (Marcus' park area)

Step1: Find actual length

The scale is 1 inch = 20 feet. The drawing length is 8 inches. So actual length = \( 8 \times 20 = 160 \) feet.

Step2: Find actual width

Drawing width is 6 inches. Actual width = \( 6 \times 20 = 120 \) feet.

Step3: Calculate area

Area of rectangle = length × width = \( 160 \times 120 = 19200 \) square feet? Wait, no, wait. Wait, 820=160, 620=120. 160120=19200? But the options have D as 19,200. Wait, but let me check again. Wait, 8 inches 20 = 160 ft, 6 inches 20=120 ft. 160120=19200. So the answer is D. Wait, but maybe I miscalculated. Wait, 820=160, 620=120. 160120: 160100=16000, 160*20=3200, total 19200. So option D.

Question 14 (Building scale drawing length)

Step1: Find scale factor

Actual height = 125 m, drawing height = 25 m. Scale factor = \( \frac{25}{125} = \frac{1}{5} \).

Step2: Find drawing length

Actual length = 80 m. Drawing length = \( 80 \times \frac{1}{5} = 16 \) m. So answer is B.

Question 15 (Triangle similarity, find x)

Step1: Identify similar triangles

Triangles ABC and DEF are similar (since they are similar triangles with scale factor 2, as 10 cm is 2 times 5 cm).

Step2: Set up proportion

For side AC (8 cm) and DF (x cm), and AB (5 cm) and DE (10 cm). The scale factor is \( \frac{10}{5} = 2 \). So \( x = 8 \times 2 = 16 \)? Wait, no, wait. Wait, triangle ABC has sides 5, 6, 8. Triangle DEF has DE=10 (which is 52), so scale factor 2. So DF (x) should be 82=16? But the options have 12? Wait, maybe I mixed up the sides. Wait, triangle ABC: AB=5, BC=8, AC=6? Wait, the diagram: A to B is 5, B to C is 8, A to C is 6? Wait, no, the first triangle: A, B, C. AB=5, BC=8, AC=6? Wait, then DE=10 (AB corresponds to DE), so scale factor is 10/5=2. Then DF corresponds to AC? Wait, no, maybe the sides are AB=5, AC=6, BC=8? Wait, the second triangle: DE=10, DF=x, EF=y. So if AB=5, DE=10 (scale 2), then AC=6, so DF=62=12? Ah, that's option C. So I misassigned the sides. So AB (5) corresponds to DE (10), AC (6) corresponds to DF (x), so x=62=12. So answer is C.

Question 14 (Building)

Answer:

B. 16 m

Question 13 (Park)