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Question
In ΔABC, B − D − C and BD = 7, BC = 20, then find the following ratio.
(i) `"A(ΔABD)"/"A(ΔADC)"`
(ii) `"A(ΔABD)"/"A(ΔABC)"`
(iii) `"A(ΔADC)"/"A(ΔABC)"`
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Solution
Draw AE ⊥ BC, B – E – C.
BC = BD + DC ......[B – D – C]
∴ 20 = 7 + DC
∴ DC = 20 − 7 = 13
(i) ΔABD and ΔADC have same height AE.
`"A(ΔABD)"/"A(ΔADC)" = "BD"/"DC"` .....[Triangles having equal height]
∴ `"A(ΔABD)"/"A(ΔADC)" = 7/13`
(ii) ΔABD and ΔABC have same height AE.
`"A(ΔABD)"/"A(ΔABC)" = "BD"/"BC"` ......[Triangles having equal height]
∴ `"A(ΔABD)"/"A(ΔABC)" = 7/20`
(iii) ΔADC and ΔABC have same height AE.
`"A(ΔADC)"/"A(ΔABC)" = "DC"/"BC"` ......[Triangles having equal height]
∴ `"A(ΔADC)"/"A(ΔABC)" = 13/20`
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