Question

triangle QRS is an equilateral triangle. If QR is seventeen more than twice x, RS is 19 less than six times x, and QS is one less four times x, find x and measure of each side.​

Answer 1

Value of x is 9 and measure of each side is 35 units.

SOLUTION:

Given, Triangle QRS is an equilateral triangle.  

QR is seventeen more than twice x, $\rightarrow QR = 17 + 2x$

RS is 19 less than six times x, $\rightarrow RS = 6x-19$

And QS is one less four times x, $\rightarrow QS = 4x-1$

We have to find x and measure of each side.

Now, we know that, sides of equilateral triangle are equal,  

Then $QR = QS \rightarrow 17 + 2x = 4x-1 \rightarrow 4x-2x = 17 + 1 \rightarrow 2x = 18 \rightarrow x = 9$

So, value of x is 9.

$\begin{array}{l}{\text { Now, } \mathrm{QR}=17+2(9)=17+18=35} \\\\ {\mathrm{RS}=6(9)-19=54-19=35} \\\\ {\mathrm{QS}=4(9)-1=36-1=35}\end{array}$

Hence, value of x is 9 and measure of each side is 35.