Problem 15
The general format for these types of problems is
A/B = C/D
One way to set things up is to notice how the horizontal sides are 15 and 6 for the large and small triangles respectively. So A/B = 15/6
At the same time, we can say C/D = 20/x since the longer diagonal is 20 and the shorter diagonal is x (notice how we divide in the same order of long over short)
A/B = C/D updates to 15/6 = 20/x
Cross multiply to solve for x
15/6 = 20/x
15*x = 6*20
15x = 120
x = 120/15
x = 8
Answer: x = 8
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Problem 16
A = Long horizontal side = x
B = Short horizontal side = 24
A/B = x/24
C = long diagonal side of larger triangle = 20+12 = 32
D = short diagonal side of smaller triangle = 20
C/D = 32/20
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A/B = C/D
x/24 = 32/20
20x = 24*32
20x = 768
x = 768/20
x = 38.4
Answer: x = 38.4
side notes:
- 38.4 = 38 & 2/5 as a mixed number
- 38.4 = 192/5 as an improper fraction
