If PQR is an equilateral triangle, PQ=18x+1, QR=24x-17, and PR=15x+10, find x and the measure of each side.

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Respuesta :

Erlea Erlea · Answer 1 · 2020-10-01T13:00:59+02:00

Answer

QR= PQ= PR

18x+1= 24x-17

18x-24x= -17-1

-6x= -18

x= 3

QR= 24(3)-17= 55

PQ= 18(3)+1= 55

PR= 15(3)+10=55

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CHERLYNnotCHERRY CHERLYNnotCHERRY · Answer 2 · 2020-10-01T13:05:17+02:00

Answer:

The value of x is 3. The length of PQ, QR and PR are 55.

Step-by-step explanation:

Given that the lengths in an equilateral triangle are all the same. We can assume that PQ = QR = PR. So we can choose any 2 lengths and compare it :

[tex]PQ = QR[/tex]

[tex]18x + 1 = 24x - 17[/tex]

[tex]1 + 17 = 24x - 18x[/tex]

[tex]6x = 18[/tex]

[tex]x = 18 \div 6[/tex]

[tex]x = 3[/tex]

Next, we have to substitute x = 3 into the expressions :

[tex]PQ = 18(3) + 1 = 55[/tex]

[tex]QR = 24(3) - 17 = 55[/tex]

[tex]PR = 15(3) + 10 = 55[/tex]