Math, asked by Ankan2007, 7 months ago

AB=DC=20cm. AE=3cm. Area of AEFD= area of EBCF. Prove that DF=17 cm.

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Answered by amitnrw
0

Given : AB=DC=20cm. AE=3cm. Area of AEFD= area of EBCF.  

To find : Prove that DF=17 cm

Solution:

AB=DC=20 cm

AE = 3 cm

EB = AB - AE = 20 - 3 = 17 cm

Let say

DF = x  cm  =>  CF = DC - DF = 20  - x  cm

Height  = h cm  

Area of trapezium AEFD

= (1/2) ( AE +  DF) * height

= (1/2) ( 3 + x) * h

Area of trapezium EBCF

= (1/2) ( EB +  CF) * height

= (1/2) ( 17 + 20 - x ) * h

= (1/2) ( 37 - x ) * h

Area of AEFD= area of EBCF

=> (1/2) ( 3 + x) * h  = (1/2) ( 37 - x ) * h

=> 3 + x = 37 - x

=>  2x = 34

=> x = 17

DF  = 17 cm

QED

Hence proved

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