Question

ABCD is a rectangle .length AB=3X+2units. Breath BC=y-2,CD=x+10,DA=3y-10 then find the length of the diagonal.

Answer 1

As ABCD is a   Rectangle,

length = AB = CD

Breadth = BC = DA
_____________________

Length,


AB = CD

3x + 2 = x + 10 

3x -x = 10 -2 

2x = 8

x =8/2 

x = 4 
__________________

Breadth,

BC = DA 

y-2 = 3y -10 

-2 + 10 = 3y - y 

8 = 2y 

8/2 = y 

4 = y 

_______________

length  = 3x + 2 
             = 3(4) + 2 
             = 12+ 2 
             =  14 units

breadth = y - 2 
              =  4 - 2 
              =  2  units

Now,

By Pythagoras Theorem,

Length² + breadth² = Diagonal²

14² + 2² = Diagonal²

196 + 4 = Diagonal²

200 = Diagonal²

√200 = Diagonal 

10√2 units= Diagonal


i hope this will help you


-by ABHAY