Question

11/17/25, 12:35 am
finding the missing side lerg
hide answer choices
answers:
a. 14 m
b. 8 m
c. 12 m
d. 6 m
triangle 1
triangle 2

Explanation:

Step1: Identify similar triangles

The two triangles are similar (assumed from the problem context of finding a missing side, likely due to similarity). For similar triangles, the ratios of corresponding sides are equal. Let's find the ratio of sides from Triangle 1 and Triangle 2. First, find the ratio of the longest sides: Triangle 1 has a side of 40 m, Triangle 2 has a side of 10 m. So the scale factor is $\frac{10}{40}=\frac{1}{4}$? Wait, no, maybe another pair. Wait, Triangle 1: sides 32 m, 36 m, 40 m? Wait, no, the labels: Triangle 1 has sides, let's see, the sides are 32 m (maybe WG?), 36 m (WD?), 40 m (DG?). Triangle 2 has sides 9 m (AC), 10 m (CT), and we need to find the missing side (maybe AT or AC? Wait, no, the missing side is probably the side corresponding to 36 m? Wait, let's check the sides. Wait, maybe the sides of Triangle 1: 32, 36, 40. Triangle 2: 9, x, 10. Wait, no, maybe the ratio is from Triangle 1 to Triangle 2. Let's take the side of 40 m in Triangle 1 and 10 m in Triangle 2: ratio is 40/10 = 4. So Triangle 1 is 4 times larger than Triangle 2. Then the side of 36 m in Triangle 1 should correspond to a side in Triangle 2: 36 / 4 = 9? No, wait Triangle 2 has a side of 9 m. Wait, maybe the side of 32 m in Triangle 1: 32 / 4 = 8? Wait, no, let's re-examine. Wait, maybe the sides are: Triangle 1: 32, 40, and 36? Wait, no, the labels: Triangle 1: vertices W, G, D? Wait, the first triangle: let's say sides: WG = 32 m, GD = 40 m, WD = 36 m. Triangle 2: AC = 9 m, CT = 10 m, AT =? Wait, no, maybe the corresponding sides: GD (40 m) corresponds to CT (10 m), so ratio is 40/10 = 4. Then WG (32 m) corresponds to AC? No, AC is 9 m. Wait, maybe WD (36 m) corresponds to AC (9 m)? 36/9 = 4. Ah, yes! So 36 m in Triangle 1 corresponds to 9 m in Triangle 2, so the scale factor is 9/36 = 1/4? Wait, no, scale factor from Triangle 1 to Triangle 2 is 9/36 = 1/4. Then the side of 32 m in Triangle 1 (WG) would correspond to a side in Triangle 2: 32 * (1/4) = 8 m. Wait, but the answer choices have 8 m as option B. Wait, let's check again.

Wait, maybe the sides: Triangle 1: 32, 36, 40. Triangle 2: x, 9, 10. Wait, no, the sides of Triangle 2 are 9, 10, and the missing side. Let's find the ratio between the triangles. Let's take the side of 40 in Triangle 1 and 10 in Triangle 2: 40/10 = 4. So Triangle 1 is 4 times Triangle 2. Then the side of 32 in Triangle 1: 32/4 = 8. The side of 36 in Triangle 1: 36/4 = 9. Oh! So Triangle 2 has a side of 9 (which is 36/4) and 10 (which is 40/4), so the missing side should be 32/4 = 8. So the missing side is 8 m, which is option B.

Step2: Calculate the missing side

Using the scale factor. Since the triangles are similar, the ratio of corresponding sides is equal. Let the missing side be \( x \). We find the ratio of a known corresponding pair. Let's take the side of length 40 m in Triangle 1 and 10 m in Triangle 2: ratio \( r = \frac{10}{40}=\frac{1}{4} \)? No, wait, if Triangle 1 is larger, then the ratio of Triangle 2 to Triangle 1 is \( \frac{10}{40}=\frac{1}{4} \). Then the side of 32 m in Triangle 1 corresponds to \( 32 \times \frac{1}{4}=8 \) m in Triangle 2. Alternatively, take the side of 36 m in Triangle 1 and 9 m in Triangle 2: ratio \( \frac{9}{36}=\frac{1}{4} \), same ratio. Then \( 32 \times \frac{1}{4}=8 \) m.

Answer:

B. 8 m