Question

2) AABCD ~ AEFGH

Use the information given to find the missing side of a figure
A)
3
x + 3
F)
x+4
E)
C)
5
B)
>H)

Answer 1

Step 1: Judging by the relative lengths of the sides of the two triangles, we can conclude that A corresponds to T, B to S, and C to R, which we can write as

△

A

B

C

∼

△

T

S

R

.

In particular, the smallest sides

A

B

and

T

S

are corresponding sides with known lengths, so we form the ratio of their side lengths

9

15

. Remember that all ratios of corresponding side lengths are equal.

Step 2: Next we form a ratio that involves

x

. Since

B

C

and

S

R

are corresponding sides, we know that the ratio of their side lengths equals the ratio from Step 1:

18

x

=

9

15

Step 3: Finally, we cross-multiply and solve for

x

:

x

⋅

9

=

18

⋅

15

9

x

=

270

x

=

270

9

=

30

That is, the missing side length is 30.