the length of a rectangle exceeds its breadth by 7 cm .if the length is decreased by 4cm and breadth is increased by 3cm , the area of the new rectangle is the same as the original rectangle . find the length and breadth of the rectangle .
Answers
Let L be length and B be breath of the rectangle.
As per the condition :
(L-4) = (B+3) + 7
hence,
L - B = 14 -------> eqn 1
also area remains same, so :
L * B = (L-4)* (B+3)
L*B = L*B + 3L - 4B - 12
3L - 4B = 12 -------> eqn 2
Solving equation 1 and 2 by elimination method, we get :
L = 42, B =28
Solution:-
given:-
• The length of the rectangle exceeds it's breadth by 7cm.
• If the length is decreased by 4cm and the breadth is increased by 3cm.
• The area of new rectangle is the same as the area of original rectangle.
Find:-
• The length and breadth of the original rectangle = ?
Formula:-
=> Area of rectangle
= length(L) × breadth(B)
Now, by given,
let, x be the breadth of rectangle so,
for original rectangle.
• breadth = B1 = x ........ ( 1 )
• length = L1 = x + 7 ........ ( 2 )
so, now....
for new rectangle
• breadth = B2 = x + 3 ........ (3)
• length = L2 = x + 7 - 4 ....... ( 4 )
we know,
=> (Area of new rectangle) = (Area of oringinal rectangle)
=> L2 × B2 = L1 × B1
=>( x + 7 - 4 ) ( x + 3 ) = ( x + 7) ( x )
=> ( x + 3 ) ( x + 3 ) = x² + 7x
=> ( x + 3 )² = x² + 7x
=> x² + 6x + 9 = x² + 7x
=> x² - x² + 6x - 7x + 9 = 0
=> - x + 9 = 0
=> - x = - 9
=> x = 9
From ( 1 ),
• breadth = x = 9 cm.
From ( 2 ),
• length = x + 7
• length = 9 + 7
• length = 16 cm.
Hence length and breadth of original rectangle is 16cm and 9cm respectively.
i hops it helps you.