Ratio and Proportion — Mathematics STD 10 — Question
ICSE BoardEnglish MediumSTD 10MathematicsRatio and Proportion2 Marks
Question
Find the third proportional to:
$\frac{a}{b}+\frac{b}{c}, \sqrt{a^2+b^2}$.
✓
Answer
Let x be the third proportional then
$\frac{a}{b}+\frac{b}{c}, \sqrt{a^2+b^2}=\sqrt{a^2+b^2}: x $
$\Rightarrow \frac{a^2+b^2}{a b}: \sqrt{a^2+b^2}=\sqrt{a^2+b^2}: x$
$ \Rightarrow \frac{a^2+b^2}{a b \sqrt{a^2+b^2}}=\frac{\sqrt{a^2+b^2}}{x} $
$ \Rightarrow x =\frac{a b\left(a^2+b^2\right)}{\left(a^2+b^2\right)}$
$ \Rightarrow x = ab.$
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