Question

If triangle PQR is an equilateral triangle, solve x and y.

PQ is 14y-59
QR is 9y+1
RP is 11y-23
Angle R is 7x-3

20 POINTS

Answer 1

Answer: x= 9 and y= 12

Explanation:

Given : Triangle PQR is an equilateral triangle.

PQ is 14y-59

QR is 9y+1

RP is 11y-23

Angle R is 7x-3 (1)

We know that , In an equilateral triangle

All sides are equal.

⇒ PQ = QR

⇒ 14y-59 = 9y+1

⇒ 14y-9y =1+59 [Subtract 9y and add 59 on both sides]

⇒ 5y=60

⇒ y= 12 [Divide both sides by 5]

All angle angles of equilateral triangle are equal and have measure 60° .

⇒ Angle R = 60°

⇒ 7x-3= 60 [From (1)]

⇒ 7x= 63 [Add 3 on both sides]

⇒ x= 9 [Divide both sides by 7]

Hence, the value of x= 9 and y= 12.

Answer 2

x = 9 and y = 15

Explanation:

An equilateral triangle, all sides and angles are congruent and each angle is equal 60 degrees

PQR is an equilateral triangle

So

PQ = QR = RP

Given:

PQ is 14y-59

QR is 9y+1

RP is 11y-23

Angle R is 7x-3

PQ = QR

Plug in

14y-59 = 9y+1

5y = 60

y = 15

Angle R is 7x-3, also <R = 60

So

7x - 3 = 60

7x = 63

x = 9

Answer

x = 9 and y = 15