Question

Given the two polygons are similar, how do I calculate the value of x?

Answer 1

@ganeshie8

Answer 2

If they are similar, the ratios of their sides are equal. You can write this in two different ways: one is that 5:7 = x:9, another is that 5:x = 7:9

Can you do it from there?

Answer 3

@whpalmer4 Could you elaborate a bit further please? Sorry, I just started geometry b and I am pretty rusty.

Answer 4

You don't understand how to solve given those ratios, or you don't understand how I could write those relationships?

Answer 5

How do I solve them?

Answer 6

@whpalmer4

Answer 7

Okay, it's just a pair of fractions that are equal.

\[\frac{5}{7} = \frac{x}{9}\]Do you remember the technique of cross-multiplication? If the fractions are equal, the numerator of the first fraction * the denominator of the second must equal the denominator of the first * the numerator of the second.

Answer 8

That gives us\[5*9=7*x\]

Answer 9

@whpalmer4 So the answer would be approximately 6.43?

Answer 10

Yes, though I would probably leave it as a fraction unless a decimal was requested, or at least write it as an equivalent, such as

\[x = \frac{45}{7}\approx 6.42857\]

Answer 11

@whpalmer4 Ok. Thanks so much for the help!

Answer 12

That way, if the answer gets used in another step or problem, you can use the exact version (here, the fraction) instead of introducing some rounding error in the middle of the overall calculation. Also, you may be able to recognize common factors, etc. later in the problem if you keep it in the fraction form, whereas if you see 0.142857 in your problem, are you going to realize that means something was divided by 7?

Answer 13

You're welcome!

Answer 14

As an exercise, you should solve the problem with the other pair of possible ratios, just to convince yourself that it really does work either way.

Answer 15

Ok thanks!