# If 15 a 2 + 4 B 2 15 a 2 − 4 B 2 = 47 7 Then Find the Value of Following Ratio. - Algebra

Sum

If (15a^2 + 4b^2)/( 15a^2 - 4b^2) = 47/7 then find the value of following ratio.
a/b

#### Solution

(15a^2 + 4b^2)/( 15a^2 - 4b^2) = 47/7
Applying componendo and dividendo, we get
[(15a^2 + 4b^2) + ( 15a^2 - 4b^2)]/[(15a^2 + 4b^2) - ( 15a^2 - 4b^2)] = [47 + 7]/[47-7]

⇒ [15a^2 + 4b^2 +15a^2 - 4b^2]/[15a^2 + 4b^2 - 15a^2 + 4b^2] =54/40

⇒ (30a^2)/(8b^2) = 27/20

⇒ a^2/b^2 = (27 xx 8)/( 20 xx 30) = 9/25

⇒ a/b = sqrt( 9/25) = 3/5

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#### APPEARS IN

Balbharati Mathematics 1 Algebra 9th Standard Maharashtra State Board
Chapter 4 Ratio and Proportion
Practice Set 4.3 | Q 2.1 | Page 70