Question

Can someone please help me? I will fan an medal!!

Answer 1

The ABC Toy Company is creating two similar pieces for a board game as shown below. Find the value of b that makes the two pieces similar.

Answer 2

Notice that one pair of corresponding sides of these two triangles are dimensioned.
What is the ratio of these dimensions? Could you now pick an appropriate value for side b so that the ratio between ON and LQ is the same as that between OP and LM?

Answer 3

@mathmale I don't know the ratio :(

Answer 4

What are the lengths of sides OP and LN? They are clearly marked in the given diagram.

Answer 5

OP=9, LN=4

Answer 6

Right. Next, what are the lengths of OP and LM? Note that OP and LM are "corresponding sides," whereas OP and LN are not. (My bad.)

Answer 7

?

Answer 8

I'd like to help you, but very much prefer you be present and involved.

Answer 9

sorry, OP=9, LM=3

Answer 10

Now, what is the ratio between 9 and 3? 9:3 is already a ratio, but can you reduce it?

Answer 11

it can be reduced to 3

Answer 12

Actually, 3:1. 3 alone is not a ratio; 3:1 (with the colon) is a ratio.

Obviously the 9 is larger than the 3.

Next, look at the corresponding sides in the two triangles.

Answer 13

ya sorry, 3:1

Answer 14

In the smaller triangle, LN has length 4. Which side in the larger triangle corresponds to side LN?

Answer 15

OQ

Answer 16

OQ corresponds to LN

Answer 17

Right. Now, try multiplying the length of LN by 3.

Answer 18

@TheKingOfCr thankyou but I also want to figure out how to solve the problem

Answer 19

12

Answer 20

I'm sorry, try mult. the length of OQ by 3. Yes, it's 12! Can you now find the third side?

Answer 21

but I don't know the length of OQ, it just says b

Answer 22

sorry I'm confused :(

Answer 23

That's true. Our job here is to figure out what the length of side ratio is between the 2 triangles; you've done that already. It's 3:1. Now, if LN is 4, and you mult. that by 3, you get 12. Therefore, b has the value 12.

Answer 24

oooh ok that makes sense now. thank you!!

Answer 25

You're very welcome! Take care.