Question 75

The ratio of the areas of two triangles ABC and PQR is 3 : 5 and the ratio of their heights is 5 : 3. The ratio of the bases of triangle ABC to that of triangle PQR is:

Solution

Let the AreasĀ  of $$\triangle ABC$$ and $$\triangle PQR$$Ā  areĀ  $$3x:5x$$Ā 

LetĀ the HeightsĀ  of $$\triangle ABC$$ and $$\triangle PQR$$Ā  areĀ  $$5y:3y$$Ā  and Bases are $$B_{1}$$ and $$B_{2}$$ respectively.

Area ofĀ $$\triangle ABC$$ = $$\frac{1}{2} \times 5y\times B_{1}$$ andĀ Area ofĀ $$\triangle PQR$$ = $$\frac{1}{2} \times3y\times B_{2}$$

$$\thereforeĀ \frac{3x}{5x}Ā = \frac{\frac{1}{2} \times 5y\times B_{1}}{\frac{1}{2} \times3y\times B_{2}}$$

$$\Rightarrow \frac{B_{1}}{B_{2}} = \frac{9}{25}$$

$$\therefore$$Ā  Ā $$B_{1}:B_{2} = 9:25$$


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