Question

A rectangular garden 40m into 30m is surrounded from outside by a path of equal width . If the area of the path is 456m^ , find the width of the path.

Answer 1

Step-by-step explanation:

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

Answer 2

Answer: 3m

Hope its help u..