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QuestionFind QRQR if points P,Q,R,SP, Q, R, S are on a line with PQ:QR:RS=3:1:2PQ:QR:RS = 3:1:2 and PS=18PS = 18.

Studdy Solution

STEP 1

Assumptions1. The points, Q, R, and all lie on the same line segment, in that order. . The ratio of PQQRRS is equal to31.
3. The length of PS is18 units.

STEP 2

We can express the lengths PQ, QR, and RS in terms of the given ratio. Let's denote the common ratio as x. Then, we haveQ=x,QR=x,RS=2xQ =x, QR = x, RS =2x

STEP 3

According to the problem, the points, Q, R, and form a single line segment. Therefore, the sum of the lengths PQ, QR, and RS equals the length of PS. We can write this asQ+QR+RS=PSQ + QR + RS = PS

STEP 4

Substitute the expressions for PQ, QR, and RS from step2 into the equation from step3.
3x+x+2x=183x + x +2x =18

STEP 5

implify the left side of the equation to find the value of x.
x=18x =18

STEP 6

olve for x by dividing both sides of the equation by6.
x=18/6x =18 /6

STEP 7

Calculate the value of x.
x=18/6=3x =18 /6 =3

STEP 8

Now that we have the value of x, we can find the length of QR by substituting x into the expression for QR from step2.
QR=xQR = x

STEP 9

Substitute the value of x into the equation for QR.
QR=3QR =3The length of QR is3 units.

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