Question

Angle 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 than four times x, find x and measure each side.

Answer 1

The value of x is 9 ,

And The measure of each sides of equilateral i.e QR , RS , QS is 35 .

Explanation:

Given as :

Triangle QRS is an equilateral triangle

The side of triangles are , QR , RS , QS

Now, According to question

QR = 2 x + 17

RS = 6 x - 19

QS = 4 x - 1

∵ The Triangle is equilateral , then all sides are equal

So , QR = RS = QS

Or, 2 x + 17 = 6 x - 19 = 4 x - 1

Now, 2 x + 17 = 6 x - 19

So, 17 + 19 = 6 x - 2 x

Or, 36 = 4 x

∴ x =
`(36)/(4)`

I.e x = 9

So, the measure of side QR = 2 x + 17 = 2 × 9 + 17

Or, the measure of side QR = 35

The measure of side RS = 6 x - 19 = 6 × 9 - 19

Or, The measure of side RS = 35

The measure of side QS = 4 x - 1 = 4 × 9 - 1

Or , The measure of side QS = 35

Hence The value of x is 9 ,

And The measure of each sides of equilateral i.e QR , RS , QS is 35 . Answer