Question

17 what is the height of the tree? remember you can use the butterfly method or find the scale factor then use i image of tree, shadow 24 ft, wall 4 ft, shadow 6 ft
options:
a 4
b 24
c 12
d 16

18 what do you call a geometric figure that is the same shape as another figure, but not necessarily the same s
options:
a congruent figure
b scaled copy
c scale factor
d transversal figure

19 an architect makes a scale drawing of a building. she uses the scale shown.
1 centimeter = 3 meters
the length of the building in the drawing is 11 centimeters.
what is the actual length, in meters, of the building?
options:
a 4 meters
b 12 meters
c 33 meters partially visible

Explanation:

Question 17

Step1: Set up proportion

Let \( h \) be the height of the tree. The two triangles are similar, so \(\frac{h}{24}=\frac{4}{6}\)

Step2: Solve for \( h \)

Cross - multiply: \( 6h = 24\times4 \)
\( 6h=96 \)
Divide both sides by 6: \( h=\frac{96}{6}=16 \)? Wait, no, wait. Wait, \(\frac{h}{24}=\frac{4}{6}\), cross - multiply: \( 6h = 24\times4\)? No, wait, \(\frac{h}{24}=\frac{4}{6}\), so \( h=\frac{24\times4}{6}\). \( 24\div6 = 4\), \( 4\times4 = 16\)? Wait, but let's check again. Wait, the small triangle has height 4 ft and base 6 ft, the large triangle has base 24 ft. So the scale factor from small to large is \( 24\div6 = 4\). Then the height of the tree is \( 4\times4 = 16\)? Wait, but the options have D as 16. Wait, but let's do the proportion correctly. \(\frac{\text{height of tree}}{\text{base of tree's triangle}}=\frac{\text{height of wall}}{\text{base of wall's triangle}}\). So \(\frac{h}{24}=\frac{4}{6}\). Cross - multiply: \( 6h=24\times4\)? No, \( 6h = 24\times4\) is wrong. Wait, \(\frac{h}{24}=\frac{4}{6}\), so \( h=\frac{24\times4}{6}\). \( 24\div6 = 4\), \( 4\times4 = 16\). So the height of the tree is 16.

• Option A: Congruent figures have the same shape and size.
• Option B: A scaled copy has the same shape as another figure but not necessarily the same size.
• Option C: Scale factor is the ratio of corresponding side lengths of similar figures.
• Option D: Transversal is a line that intersects two or more lines, not related to figure similarity.

Step1: Understand the scale

The scale is 1 centimeter = 3 meters. This means that 1 cm on the drawing represents 3 meters in real life.

Step2: Calculate actual length

If the length on the drawing is 11 centimeters, then the actual length \( L=11\times3\) meters.
\( 11\times3 = 33\) meters.

Answer:

D. 16

Question 18