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Question

In ΔABC, express x in terms of a, b, and c
339515_478f77532ba54cf9b0b426625cbd60df.png

A
acb+c
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B
aba+c
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C
bca+b
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D
bcb+c
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Solution

The correct option is A acb+c
ABC=DEC=45o [ Given ]

AB=a,BE=b,DC=x and EC=c [ Given ]
In CDE and CAB

DEC=ABC [ Given ]

C=C [ Common angle ]

CDECAB [ By AA similarity test ]

ECBC=DEAB [ Corresponding sides of similar triangles are proportional ]

cb+c=xa

x=acb+c

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