Question

Calculate pqrst in the diagram above showing your solutions ​

Answer 1

a. p = 6

b. q = 4

c. r = 8

d. s = 10; t = 8.3

Explanation:

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

`(9)/(p) = (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 = (1)/(2)(8)`

`q = 4`

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

`(4)/(10) = (r)/(20)`

Multiply both sides by 20

`(4)/(10) * 20 = (r)/(20) * 20`

`(80)/(10) = r`

r = 8

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

`(9 + 6)/(9) = (s)/(6)`

`(15)/(9) = (s)/(6)`

Multiply both sides by 6

`(15)/(9) * 6 = (s)/(6) * 6`

`(15 * 6)/(9) = s`

s = 10

`(9 + 6)/(9) = (t)/(5)`

`(15)/(9) = (t)/(5)`

Multiply both sides by 5

`(15)/(9) * 5 = (t)/(5) * 5`

`(15 * 5)/(9) = t`

t = 8.3 (nearest tenth)