there is a footpath around a rectangular garden with kength 30m and breadth 20m. The area of the large rectangular plot including the footpath and garden is 816m². Find the width of the footpath?
Answers
Step-by-step explanation:
A rectangular garden 40 m ×30 m is surrounded from outside by a path of equal width. if the area of the path is 456 m² , find the width of the path?
ANSWER :
FOR RECTANGLE
LENGTH = 40M
BREADTH = 30M
SO AREA OF GARDEN=L×B
=40×30
=1200M²
SO LET THE SUM OF WIDTH BE X FOR THE PATH FROM BOTH SIDES
SO 2(WIDTH)=X
SO OVERALL LENGTH = (40+X)M
AND OVERALL BREADTH = (30+X)M
SO OVERALL AREA = L×B
=(40+X)(30+X)
=1200+40X+30X+X²
= (X²+70X+1200)M
NOW IT IS GIVEN THAT
AREA OF PATH=456M²
SO AREA OF PATH = OVERALL AREA-AREA OF GARDEN
456=X²+70X+1200-1200
X²+70X-456=0
So by splitting the middle term method
X²+76X-6X-456=0
X(X+76)-6(X+76)=0
(X+76)(X-6)=0
SO
X+76=0 OR X-6=0
X=-76 OR X=6
BUT BREADTH CAN NEVER BE NEGATIVE
SO X=-76 IS REJECTED
SO X=6 IS ACCEPTED
SO 2(WIDTH)=X
WIDTH=X/2
WIDTH=6/2
WIDTH=3M
HENCE THE WIDTH OF THE PATH IS 3 METRES