the length of a rectangle exceeds its breadth by 7 centimetre if the length is described by 4 cm and the breadth is increased by 3cm the area of the new rectangle is same as the original rectangle
Answers
LET THE BREADTH BE x ,
so,
LENGTH = x+7
New length = (x+7) - 4
New breadth = x + 3
B.T.P,
NEW AREA = ORIGINAL AREA
=>(x + 7- 4)(x+3) = (x+7) (x)
=> (x + 3) (x + 3) = x^2 + 7x
=> (x+3)^2 = x^2 + 7x
=> x^2 + 6x + 9 = x^2 + 7x
=> x = 9.
Therefore ,
LENGTH
= x+7
= 9+7
= 16
BREADTH = 9
For finding the length and breadth of original rectangle
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
• breadth = 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 hope it helps you.