Question

Triangles WSR and TVR are similar. Find x.

Answer 1

@ganeshie8 do you think you can help?

Answer 2

First, find the sides of triangle WSR that "match up" with triangle TVR
For example, the side WS in the first triangle "matches up" with what side in triangle TVR?

Answer 3

TV

Answer 4

now write down a "ratio" length of side WS / length of side TV

can you do that ?

Answer 5

8/12

Answer 6

and it's always good to simplify. can you simplify 8/12 ?

Answer 7

divide top and bottom by 4

Answer 8

2/3

Answer 9

next, they want to find x. In the first triangle, that means we want to use side WR, which has length x+8

WR matches up with side RT in the other triangle. side RT has length x+14

we form another ratio:
\[ \frac{x+8}{x+14} \]

Answer 10

Ok

Answer 11

now set the two ratios = to each other:
\[ \frac{2}{3}= \frac{x+8}{x+14} \]

to solve for x, I would first cross-multiply. can you do that?

Answer 12

Umm

Answer 13

cross multiply means top left times bottom right = bottom left times top right

try it

Answer 14

Yes I know, but I'm not sure of the answer. Like 2(x+14)??

Answer 15

yes, that is how you would write it.

Answer 16

but how to solve it?

Answer 17

first write down what have so far.

Answer 18

2/3=x+8/x+14....2(x+14) and 3(x+8)??

Answer 19

you should write it
2(x+14) = 3(x+8)

Answer 20

Ok

Answer 21

on the left side, "distribute" the 2. that means multiply each term inside the parens by 2

on the right side, distribute the 3

Answer 22

2x+28=3x+24 ?? I am not sure if I did that right

Answer 23

that is correct.
2x+28=3x+24

next, I would add -2x to both sides, like this:
2x - 2x + 28 = 3x - 2x + 24

and simplify. on the left side what is 2x - 2x
on the right side what is 3 x's take away 2 x's ?

Answer 24

28=x+24

Answer 25

finally add -24 to both sides and simplify

Answer 26

x=4?

Answer 27

yes

Answer 28

Thank you

Answer 29

yw