Question

Circles M and K are congruent, QR is congrent to LN. Find the length of QR

Answer 1

Given QR is congrent to LN and QR = 4x + 2 and LN = x + 7.

So, QR = LN

Hence, we can set up an equation as following:

4x + 2 = x + 7

4x + 2 - x = x + 7 - x Subtract x from each sides.

3x + 2 = 7 By simplifying.

3x + 2 - 2 = 7 - 2 Subtract 2 from each sides.

3x = 5

$\frac{3x}{3} =\frac{5}{3}$ Divide each sides by 3 to isolate x.

So, $x=\frac{5}{3}$

Next step is to plug in $x=\frac{5}{3}$ in QR = 4x+2 to get length of QR.

So, $QR = 4(\frac{5}{3})+2$

$=(\frac{20}{3})+\frac{2}{1}$ Since 2 can be written as 2/1.

By multiplying the second fraction by the common denominator 3.

$=(\frac{20}{3})+\frac{2*3}{1*3}$

$=(\frac{20}{3})+\frac{6}{3}$ By simplifying the second fraction.

$=(\frac{26}{3})$

So, $QR=\frac{26}{3}$