Calculate pqrst in the diagram above showing your solutions

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:

Cross multiply

Divide both sides by 15

p = 6

b. Based on the midsegment theorem,

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

Multiply both sides by 20

r = 8

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

Multiply both sides by 6

s = 10

Multiply both sides by 5

t = 8.3 (nearest tenth)

heudhduxhdnshenebdutbbt

step-by-step explanation:

hrhhdhdbbrurb ees

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4