SOLUTION: A rectancle JKLM is inscribed in an another rectangle ABCD such that the vertices J,K,L and M touches the side AB,BC, CD and DA respectively.where AB = 12cm and BC = 7cm. Also A

Question 28582: A rectancle JKLM is inscribed in an another rectangle ABCD such that the vertices J,K,L and M touches the side AB,BC, CD and DA respectively.where AB = 12cm and BC = 7cm. Also AJ = BK= CL= DM= x.The area of rectangle JKLM is 54cm2. Find x?
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
SEE DRAWING BELOW

LET AK=BL=CM=DN=X
AB=CD=12 AND BC=DA=7.
FIRSTLY KLMN WILL NOT BE A RECTANGLE.IT WILL BE PARALLELOGRAM AS YOU CAN SEE BELOW.
LET DC BE X AXIS AND DA BE Y AXIS WITH D AS ORIGIN.HENCE COORDINATES OF DIFFERENT POINTS ARE
D...(0,0) M..(10,0) C�(12,0) L�(12,5) B�.(12,7) K�.(2,7) A�.(0,7) N�.(0,2)
SLOPE OF MN =(0-2)/(10-0)= -1/5
SLOPE OF NK =(7-2)/(2-0)= 5/2
PRODUCT OF SLOPES =(-1/5)*((5/2)=-1/2�..SO THEY ARE NOT PERPENDICULAR.
SO KLMN IS NOT A RECTANGLE.
THEN FORMULA FOR AREA ALSO CHANGES.
LET US FIND AREAS OF 4 TRIANGLES AKN,KBL,LCM AND MDN ALL OF WHICH ARE RIGHT ANGLED TRIANGLES.
SUM OF THEM IS 84-54=30..AS THIS IS EQUAL TO AREA OF ABCD(84) - AREA OF KLMN (54)
SUM OF AREAS OF 4 TRIANGLES AKN,KBL,LCM AND MDN ARE
(1/2){X(12-X)+X(7-X)+X(12-X)+X(7-X)}=X(12-X)+X(7-X)=X(12-X+7-X)=X(19-2X)=19X-2X^2=84-54=30
2X^2-19X+30=0
2X^2-4X-15X+30=0
2X(X-2)-15(X-2)=0
(X-2)(2X-15)=0
X-2=0�.OR��X=2
2X-15=0�.OR�.X=7.5�WHICH IS BEYOND SIDES BC AND DA..SO NOT TO BE CONSIDERED.
SO X=2
RELATED QUESTIONS
What is the perimeter of rectangle jKLM with vertices j(-1,3), k(2,3), l(2,-5),... (answered by Alan3354,ikleyn)

What is the perimeter of rectangle JKLM, with vertices J(�1, 3), K(2, 3), L(2, �5),... (answered by stanbon)

In rectangle ABCD, AB=10 and BC=15. A point P inside the rectangle is such that BP=12,... (answered by mananth,ikleyn)

In the diagram, quadrilateral JKLM is a parallelogram. Which statement proves... (answered by Theo)

Parallelogram JKLM has the following coordinates: J(-6, 3), K(-3, 7), L(6, 7), and M(3,... (answered by Boreal)

J(-5,2), K(-2,6), L(5,6) and M(2,2) are the coordinates. What is the area of the... (answered by ewatrrr)

abcd is a quadrilateral inscribed in a circle. bc = cd, ab//dc and angle dbc =50°, find... (answered by Boreal,ikleyn)

ABCD is a quadrilateral inscribed in a circle. BC=CD, AB//DC and angle DBC= 50° find... (answered by ikleyn)

ABCD is a quadrilateral inscribed in a circle. BC=CD, AB//DC and LDBC= 50° find... (answered by ikleyn)