Question

If triangle pqr is and equilateral triangle, pq = 18x+1, qr = 24x-17, and pr = 15x+10, find x and the measure of each side.

Answer 1

x = 3.

Measure of each side is 55 units.

Explanation:

In an equilateral triangle, the length of all the three sides are equal.

Therefore, Side PQ = QR = PR.

⇒ 18X + 1 = 24X - 17

⇒ 24X - 18X = 18

⇒ 6X = 18

⇒ X = 3

Substituting the value of X, we get:

PQ = 18(3) + 1 = 55 Units.

QR = 24(3) - 17 = 55 units.

PR = 15(3) + 10 = 55 units.

We see the length of all the sides are equal.

Answer 2

The value of x is 3 ,

The measure of each side is 55 units .

Explanation:

Given as :

The sides of the equilateral Triangle are pq , qr , pr

The measure of side pq = 18 x + 1

The measure of side qr = 24 x - 17

The measure of side pr = 15 x + 10

∵ The triangle is equilateral then all sides are equal

i.e pq = qr = pr

So, 18 x + 1 = 24 x - 17

Or, 24 x - 18 x = 17 + 1

Or, 6 x = 18

∴ x =
`(18)/(6)`

i.e x = 3

So, Putting the value of x

The measure of side pq = 18 × 3 + 1 = 55 unit

The measure of side qr = 24 × 3 - 17 = 55 unit

The measure of side pr = 15 × 3 + 10 = 55 unit

Hence The value of x is 3 ,

And The measure of each side is 55 units . Answer