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Question
In fig. BD = 8, BC = 12, B-D-C, then `"A(ΔABC)"/"A(ΔABD)"` = ?
Options
2 : 3
3 : 2
5 : 3
3 : 4
Solution
3: 2
In ΔABC and ΔABD,
ΔABC and ΔABD have the same height. ...(Given)
The ratio of the areas of two triangles with equal heights is equal to the ratio of their corresponding bases.
∴ `"A(ΔABC)"/"A(ΔABD)" = "BC"/"BD"`
∴ `"A(ΔABC)"/"A(ΔABD)" = 12/8`
∴ `"A(ΔABC)"/"A(ΔABD)" = 3/2`.
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