Question

abcd is a rectangle length ab=3x+2 units.breadth bc=y-2,cd=x+10,da=3y-10,then find the length of the diagonal

Answer 1

Heya,
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As Given that it is a Rectangle, 

Length = ab = cd
Breadth = cd = da
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Now,

ab = cd 
3x +2 = x + 10 

3x -x = 10- 2

2x = 8 

x = 8/2

x = 4 units

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                    AND     


Breadth=  bc = ad

bc = ad 

y - 2 = 3y - 10 

-2 + 10 = 3y- y

10 - 2 = 2y 

8 = 2y 

8/2 = y 

4 =y 

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Now,

Length = 3x +2 
            = 3(4) + 2 
            =  12 + 2 
            = 14 units
         _____________

Breadth  = y - 2 
                = 4-2 
               = 2  units

By Pythagoras Theorem,

Diagonal² = Length² + breadth²

(Length of diagonal)^2 = $14^2 + 2^2$

(Length Of diagonal)^2 = 196 + 4 

(Length of diagonal)^2 = 200

Length of diagonal = 10√2 units





i hope this will help you



-by ABHAY