calculate pqrst in the diagram above showing your solutions ​

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)

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