Question

please help! I will medal!
In parallelogram PQRS, PT=x+2, TR=y, QT=2x, and TS=y+3. What is the length of the longer diagonal?

Answer 1

Do you need a letter

Answer 2

sorry i forgot to put the answer choices

Answer 3

one moment

Answer 4

A. 7
B. 10
C. 14
D. 20

Answer 5

Looks like the T is in the center, which makes QT = TS and PT = TR, so 2 equations would be needed

Answer 6

how would i go about setting up the equations

Answer 7

Like for the QT = TS, you said QT was 2x and TS was y+3, so that equation is y+3 = 2x

What would the other one be?

Answer 8

x+2=y , right?

Answer 9

Right, so now you have to find an X and Y value by using the tedious substitution method to find those values to satisfy both equations

It'll take a while, so ill work it with you

Answer 10

Oh, but first

Since we had y+3 = 2x for the first one, we have to get y by itself.

Answer 11

could y=5 ?

Answer 12

I don't know I'm not very smart

Answer 13

You did get the numeral right, but not the variable

Oh, don't be like that. This problem takes alot of time

Answer 14

so x=5 ?

Answer 15

Right! Plugging that into both those equations will get you the same y value, which is...?

Answer 16

7

Answer 17

i think

Answer 18

it is 7

Answer 19

i think

Answer 20

Correct! Now we can finally find the answer to this

So we said originally QT = TS and PT = TR, which means QT + TS is one length and PT + TR is another

So we add original lengths

(2x) + (y+3) =
(y) + (x+2) =

We know y =7 and x=5

After finding those two answer, the larger number is the longer side

Answer 21

one moment

Answer 22

so is it 7 or 14

Answer 23

so the longer side is 20 because

(2x5)+(7+3)=20

and that is greater than

(7)+(5+2)=14

Answer 24

Exactly! It's D

Answer 25

I got the answer AND I understand it! Thank you so much.

Answer 26

Anytime!