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Alexus [3.1K]
3 years ago
10

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 les

s four times x, find x and measure of each side.​
Mathematics
1 answer:
koban [17]3 years ago
5 0

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

<u>SOLUTION: </u>

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.

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