Question

Calculate pqrst in the diagram above showing your solutions ​

Answer 1

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:

$\frac{9}{p} = \frac{15}{10}$

Cross multiply

$15*p = 10*9$

$15*p = 90$

Divide both sides by 15

p = 6

b. Based on the midsegment theorem,

$q = \frac{1}{2}(8)$

$q = 4$

c. The side length of two similar triangles are proportional, therefore:

$\frac{4}{10} = \frac{r}{20}$

Multiply both sides by 20

$\frac{4}{10} \times 20 = \frac{r}{20} \times 20$

$\frac{80}{10} = r$

r = 8

d. The side length of two similar triangles are proportional, therefore:

$\frac{9 + 6}{9} = \frac{s}{6}$

$\frac{15}{9} = \frac{s}{6}$

Multiply both sides by 6

$\frac{15}{9} \times 6 = \frac{s}{6} \times 6$

$\frac{15 \times 6}{9} = s$

s = 10

$\frac{9 + 6}{9} = \frac{t}{5}$

$\frac{15}{9} = \frac{t}{5}$

Multiply both sides by 5

$\frac{15}{9} \times 5 = \frac{t}{5} \times 5$

$\frac{15 \times 5}{9} = t$

t = 8.3 (nearest tenth)