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.

The value of x is 9 ,  

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

Step-by-step 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 =

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

answer: 20

step-by-step explanation:

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.