Question

triangle QRS is an equilateral triangle if QR is 7 less than twice X RS is 61 less than 5 times x and QS is 11 more than x find X and the measure of each side

Answer 1

Answer:

QR=RS=QS=29    

Step-by-step explanation:

Given QRS is an equilateral triangle, thus all the three sides of the given triangle will be equal.

Also, from the given statement, we have

QR=2x-7, RS=5x-61 and QS=11+X

Now, As all the sides of the triangle are equal, therefore

QR=RS=QS

⇒QR=RS

⇒2x-7=5x-61

⇒-7+61=5x-2x

⇒54=3x

⇒x=18

Thus, the measure of QR=2(18)-7=29,RS=5(18)-61=29 and QS=11+18=29.

Answer 2

Answer: The answer is 29 units.

Step-by-step explanation:  As given in the question and shown in the attached figure, ΔQRS is an equilateral triangle, where the measure of the sides are given in the form of an unknown variable 'x' as follows.

$\textup{QR}=2x-7,~~\textup{RS}=5x-61,~~\textup{QS}=x+11.$

Since the triangle is an equilateral one, so all the sides must be equal to one another. So, we have

$\textup{QR}=\textup{RS}\\\\\Rightarrow 2x-7=5x-61\\\\\Rightarrow 5x-2x=61-7\\\\\Rightarrow 3x=54\\\\\Rightarrow x=18.$

Therefore,

$\textup{QR}=2x-7=2\times 18-7=36-7=29.$

Since, QR = RS = QS, so measure of each side is 29 units.

Thus, the answer is 29 units.