Mathematics
04.01.2021 13:37
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Find the length of chord QS

Find the length of chord QS
Find the length of chord QS
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julianastri6841
julianastri6841
4,7(91 marks)

Given:

QW = 12 and WS = 4x + 1

PW = 14 and WR = 3x + 3

To find:

The length of the chord QS.

Solution:

If two chords intersect inside a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

\Rightarrow QW \cdot  WS= PW\cdot WR

\Rightarrow 12 \cdot  (4x+1)=14 \cdot (3x+3)

\Rightarrow 48x+12= 42x+42

Subtract 12 from both sides.

\Rightarrow 48x+12-12= 42x+42-12

\Rightarrow 48x= 42x+30

Subtract 42x from both sides.

\Rightarrow 48x-42x= 42x+30-42x

\Rightarrow 6x= 30

Divide by 6 on both sides, we get

⇒ x = 5

QS = QW + WS

      =12+4x+1

      =12+4(5)+1

      =13+20

      = 43

The length of QS is 43.

lucylubugg
lucylubugg
5,0(37 marks)
72 miles is how much he would run 

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