Question

Triangle BCD is similar to triangle ACE. If the triangles are isosceles, what is the length of AB?

F.) 16cm
G.) 11cm
H.) 40cm
J.) 35cm

Answer 1

Answer: 35 cm which is choice J

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Step-by-step explanation:

AE = 22 and BD = 2.75
The triangles are similar so we can divide the two values (larger over smaller) to get: 22/2.75 = 8
This means that AE is 8 times larger than BD
AE = 8*BD

BC = 5 because CD = 5 (we have an isosceles triangle BCD)

AC is going to be 8 times longer than BC based on what we found above
AC = 8*BC
AC = 8*5
AC = 40

We can break up AC into AB+BC (think of it like gluing the two pieces together)

AC = AB+BC
40 = AB+5
40-5 = AB
35 = AB
AB = 35