Question

I really need help with this please and thank you!

Answer 1

Fear not, if you call upon Jesus' name you are saved.

Explanation:

Okay well we are given two shapes correct?

Yes, so we have the value of one side of the shape, that is shape ABCDE.

Now when you look at the question it states, that they are *similar*

What does this mean?

The figures are equal to each other by one ratio (value).

Definition of similar: Two shapes that are not congruent but have the same value of each sides by a ratio.

So if what they are saying is true all the other sides of the shape have that same ratio.

SO because we know this we multiply the sides of the shape JKLMN by that ratio

But what is the ratio?

Well you can do this either way.

You can divide 20 by 8

or 8 by 20

BUT

Because we already have the smaller values and we need to find the bigger ones, we need to use the bigger value, because if we don't the we will just get smaller values which will make the figure even smaller.

So the bigger ratio is 20/8 (Why are we using 20 and 8? They have the same side so that's why we are using them instead of 7 or 5. We need to find the ratio between the figures, and we have both in 20 and 8.)

Lets use it:

20/8= 2.5

NOW if we multiply every value by this number, like 7 and 5. We will get the values q and r

7 x 2.5= 17.5

5 x 2.5= 12.5

Extra Note:

Remember how I said to use the bigger value? Let me show you why:

Using the smaller value would be the scale 8/20

8/20= 0.4

Now if we multiplied 7, and 5 by 0.4 look at what we would get

7 x 0.4= 2.8

5 x 0.4= 2

How do we know these are wrong though?

We are getting a smaller figure when we are trying to get the bigger figure as shown by the graph

For this reason using the ratio 8/20 would just be used to find a smaller figure from a bigger figure.

So the answer is B, but believe in God im telling you I used to struggle with math too but he helped me. God bless.

Answer 2

B. q = 17.5 and r = 12.5

Explanation:

You want the lengths of sides q=DE and r=CD in figure ABCDE that is similar to JKLMN with sides EA=20, LM=5, MN=7, NJ=8.

Corresponding sides

The similarity statements tell us the corresponding sides are ...

• AB and JK
• BC and KL
• CD = r and LM = 5
• DE = q and MN = 7
• EA = 20 and NJ = 8

Proportional

This means we can write the proportion ...

EA/NJ = DE/MN = CD/LM

20/8 = q/7 = r/5

q = 7(20/8) = 17.5

r = 5(20/8) = 12.5

The unknown lengths are q = 17.5 and r = 12.5, choice B.

Analysis

As an alternative to doing any math, we can simply examine the answer choices for reasonableness. We can see that the shortest-to-longest order of the side lengths is ...

5, 7, 8 ⇔ r, q, 20

This means we can reject any answer choices that have r > q. That eliminates choices A, C, D, leaving only the correct choice, B.

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