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ICSE Class 10 Frank Maths Ratio and Proportion
Ratio and Proportion

If a, b, c and d are in proportion, prove that: (iii)\[({{\mathbf{a}}^{\mathbf{4}}}~+\text{ }{{\mathbf{c}}^{\mathbf{4}}}):\text{ }({{\mathbf{b}}^{\mathbf{4}}}~+\text{ }{{\mathbf{d}}^{\mathbf{4}}})\text{ }=\text{ }{{\mathbf{a}}^{\mathbf{2}}}{{\mathbf{c}}^{\mathbf{2}}}:\text{ }{{\mathbf{b}}^{\mathbf{2}}}{{\mathbf{d}}^{\mathbf{2}}}\] (iv) \[\frac{{{a}^{2}}+ab}{{{c}^{2}}+cd}=\frac{{{b}^{2}}-2ab}{{{d}^{2}}-2cd}\]

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It is given that a, b, c, d are in proportion Consider a/b = c/d = k a = b, c = dk (iii) \[({{a}^{4}}~+\text{ }{{c}^{4}}):\text{ }({{b}^{4}}~+\text{ }{{d}^{4}})\text{ }=\text{...

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10. Find the triplicate ratio of the following: The ratio is used for comparing two quantities of the same kind. The ratio formula for two numbers says a and b is given by a:b or a/b. When two or more such ratios are equal, they are said to be proportion. The concept of ratio and proportion is majorly based on ratios and fractions. (iii)$\sqrt{15}:\sqrt{18}$ (iv) ${}^{3}{{\sqrt{\left( ab \right)}}^{2}}:{}^{3}\sqrt{\left( {{a}^{2}}b \right)}$

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Given, $\sqrt{15}:\sqrt{18}$ $={{\left( \sqrt{15} \right)}^{3}}:{{\left(\sqrt{18} \right)}^{3}}$ $=15\sqrt{5}:18\times3\sqrt{2}$ $=5\sqrt{15}:18\sqrt{2}$ Therefore, triplicate ratio is...

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