Question

ABCD is a parallelogram.Solve for x&y
AB=x+y, BC=x-y, CD=10, AD=5.

Answer 1

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• ABCD is a //gm
• in which AB=X+Y ,BC=X-Y,CD=10 and AD=6

${\sf{\green{\underline{\large{To\:find}}}}}$

• Value of X and y

${\sf{\pink{\underline{\Large{Explanation}}}}}$

Diagram

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(8.6,3){\large{A}}\put(7.7,0.9){\large{B}}\put(9.5,0.7){\sf{\large{6}}}\put(11.1,0.9){\large{C}}\put(8,1){\line(1,0){3}}\put(11,1){\line(1,2){1}}\put(9,3){\line(3,0){3}}\put(7.7,2){\large{ \sf\:10 }}\put(8,1){\line(1,2){1}}\put(12.1,3){\large{D}}\put(8,1){\line(2,1){4}}\put(11,1){\line(-1,1){2}}\end{picture}$

property of parallelogram

• Opposite sides are equal
• opposite angles are equal
• Diagonals equal to each other.

From this we conclude that

AB=CD

BC=AD

According to the question

• AB=X+Y ,
• BC=X-Y,
• CD=10 and
• AD=6

Now

X+Y=10____(1)

X-Y=6____(2)

solving equation (1) and (2)

• By Elimination method

X+Y=10

X-Y=6

_____

=>2x=16

X=8

Putting the value in equation 1

X+Y=10

=>8+y=10

=>y=2