Question

The two triangles are similar. There are two possible values of x. Work out each of these values. State both assumptions you make in your working. You must state which two triangles you are assuming to be similar.

Answer 1

This will give you 5/5

x = 17

x=2

Assuming triangle ABE is similar to ACD

Assuming traingle ABE is similar to ADC

Explanation:

18/10 = 1.8 (S.F)

15 x 1.8 = 27

27-10 = 17

x = 17

15+3=18

18/15= 1.2 (S.F)

10x1.2= 12

12-10=2

x=2

Assuming triangle ABE is similar to ACD

Assuming triangle ABE is similar to ADC

Answer 2

• ΔABE ~ ΔACD, x = 2
• ΔABE ~ ΔADC, x = 17

Explanation:

ΔABE ~ ΔACD

AC/AB = AD/AE

(10+x)/10 = (15+3)/15

1 +x/10 = 1 +0.2 . . . expand each ratio

x = 10(0.2) . . . . . . . subtract 1 and multiply by 10

x = 2

__

ΔABE ~ ΔADC

AC/AE = AD/AB

(10+x)/15 = (15+3)/10

10 +x = 27 . . . . . . . . multiply by 15

x = 17 . . . . . . . . . . . . subtract 10

_____

Additional comment

The triangles can be declared similar in 6 ways, but it does no good to match a marked side with an unmarked side. Hence, only two of the possible similarity statements will result in a solution for x.