Question

What value of x will make the triangles similar by the SSS similarity theorem?


15.9

59

77

96.8

Answer 1

I would write a proportion:
\[ \frac{20}{44} = \frac{35}{x} \]
or, flipping both ratios
\[ \frac{44}{20} = \frac{x}{35} \]
to find x, multiply both sides by 35, like this
\[ 35 \cdot \frac{44}{20} = \frac{x}{\cancel{35}} \cdot \cancel{35} \\
35 \cdot \frac{44}{20} =x
\]

Answer 2

now you do arithmetic
divide top and bottom by 4, to simplify 44/20 to 11/5
you now have
\[ x = 35 \cdot \frac{11}{ 5} \]
now divide 5 into 35 to get 7
\[ x = 7 \cdot 11\]

Answer 3

Why don't you do 35 x 11 ?

Answer 4

do you mean why not do 35*11 in this step?
\[ x = 35 \cdot \frac{11}{ 5} \]

Answer 5

yes

Answer 6

you could, but it's easier to try to simplify i.e. divide first
if you did 35*11 = 385
and the problem becomes 385/5
those steps are harder (for me, anyway) than doing the divide first:

35/5 * 11 = 7*11= 77
(I can do that in my head. The first way, I need paper or a calculator)

Answer 7

Okay thank you!!