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Question

In the given figure, ABC is a triangle with EDB=ACB. Prove that ΔABCΔEBD.IfBE=6 cm,EC=4 CM,bd=5 cmandareaofΔBED=9cm2, calculate: [4 MARKS]
(i) Leight of AB
(ii) Area of ΔABC.

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Solution

Application of theorems: 2 Marks
Calculation: 2 Marks
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In ΔABCandΔEBD.
ACB=EDB[Given] B=B[Common]So,ΔABCΔEBC[AA similarity]
Given BE=6CM,ec=4CM,BD=5cm,andareaofΔBED=9cm2
(i) ΔABCΔEBDABEB=ACED=BCBCAB6=ACED=6+45AB6=105AB=10×65=12 cm(ii)Area of ΔABCArea of ΔEBD=AB2EB2Area of ΔABC9=(12)2(6)2Area of ΔABC9=14436Area of ΔABC=9×1443636 cm2

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