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# Find the Fourth Proportion to the Following: - ICSE Class 10 - Mathematics

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#### Question

Find the fourth proportion to the following:

(p2q - qr2 ), (pqr - pr2 ) and (pq2 - pr2)

#### Solution

Let x be the fourth proportion

("p"^2"q" - "qr"^2) : ("pqr" - "pr"^2) :: ("pq"^2 - "pr"^2) :  x

⇒ ("p"^2"q" - "qr"^2) xx "x" =  ("pqr" - "pr"^2) xx ("pq"^2 - "pr"^2)

⇒ x = (("pqr" - "pr"^2) xx ("pq"^2 - "pr"^2))/(("p"^2"q" - "qr"^2))

⇒ x = ("pr"("q" - "r") xx "p"("q"^2 - "r"^2))/("q"("p"^2 - "r"^2))

⇒ x = ("pr"("q - r") xx "p"("q - r")("q + r"))/("q"("p"^2 - "r"^2))

⇒ x = ("p"^2"r" ("q" - "r")^2 ("q" + "r"))/("q" ("p"^2 - "r"^2))

The fourth proportion is ("p"^2"r" ("q" - "r")^2 ("q" + "r"))/("q" ("p"^2 - "r"^2))

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#### APPEARS IN

Frank Solution for Frank Class 10 Mathematics Part 2 (2016 to Current)
Chapter 9: Ratio and Proportion
Exercise 9.2 | Q: 2.3

#### Video TutorialsVIEW ALL [1]

Solution Find the Fourth Proportion to the Following: Concept: Proportions.
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