A square and a triangle have equal areas. If the ratio side of square and the height of triangle is 2:3, find the ratio of base to height.

2;3

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4:3

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4:5

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8:9

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Solution

The correct option is A 8:9
According to the problem,
$a^{2} = \frac{1}{2} \times b \times h$

$\frac{a}{h} = \frac{2}{3}$ or $a = \frac{2}{3} h$

$\frac{1}{2} h b = a^{2}$
Subsituting $a = \frac{2}{3} h$ and on simplifying we get,
$b = \frac{8}{9} h$

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