Question

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

Answer 1

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

Answer 2

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 :

$PQ = QR$

$18x + 1 = 24x - 17$

$1 + 17 = 24x - 18x$

$6x = 18$

$x = 18 \div 6$

$x = 3$

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

$PQ = 18(3) + 1 = 55$

$QR = 24(3) - 17 = 55$

$PR = 15(3) + 10 = 55$