Answer:
a. p = 6
b. q = 4
c. r = 8
d. s = 10; t = 8.3
Step-by-step explanation:
1. a. The side length of two similar triangles are proportional, therefore:
[tex] \frac{9}{p} = \frac{15}{10} [/tex]
Cross multiply
[tex] 15*p = 10*9 [/tex]
[tex] 15*p = 90 [/tex]
Divide both sides by 15
p = 6
b. Based on the midsegment theorem,
[tex] q = \frac{1}{2}(8) [/tex]
[tex] q = 4 [/tex]
c. The side length of two similar triangles are proportional, therefore:
[tex] \frac{4}{10} = \frac{r}{20} [/tex]
Multiply both sides by 20
[tex] \frac{4}{10} \times 20 = \frac{r}{20} \times 20 [/tex]
[tex] \frac{80}{10} = r [/tex]
r = 8
d. The side length of two similar triangles are proportional, therefore:
[tex] \frac{9 + 6}{9} = \frac{s}{6} [/tex]
[tex] \frac{15}{9} = \frac{s}{6} [/tex]
Multiply both sides by 6
[tex] \frac{15}{9} \times 6 = \frac{s}{6} \times 6 [/tex]
[tex] \frac{15 \times 6}{9} = s [/tex]
s = 10
[tex] \frac{9 + 6}{9} = \frac{t}{5} [/tex]
[tex] \frac{15}{9} = \frac{t}{5} [/tex]
Multiply both sides by 5
[tex] \frac{15}{9} \times 5 = \frac{t}{5} \times 5 [/tex]
[tex] \frac{15 \times 5}{9} = t [/tex]
t = 8.3 (nearest tenth)
