Question

the+perimeter+of+a+rectangular+plot+is+32+metres+if+the+length+is+increased+by+2+metres+and+breadth+is+decreased+by+1+m+the+area+of+plot+remains+same+find+the+length+and+breadth+of+the+plot

Answer 1

Answer:

The length of the plot is 10m and the breadth is 6m

Step-by-step explanation:

Let L be the length of the original rectangle, and

let B be the breadth of the original rectangle.

Thus, perimeter = 2*(L+B)

2*(L+B) = 32

L+B = 16 ...................(Eqn 1)

Area of rectangle = L*B

Now,

length is increased by 2, so new length = L+2

breadth is decreased by 1, so new breadth = B-1

New area = (L+2)*(B-1)

                 = L*B - L + 2B -2

                 = Old Area - L + 2B - 2

But, New Area = Old Area

Thus,

0 = -L + 2B -2

0 = -3L + 2L + 2B -2            (Rewriting -L as -3L+2L)

0 = -3L + 2(L+B) - 2

0 = -3L + 32 - 2

0 = -3L + 30

3L = 30

L = 10

Substituting for L in Eqn 1, we get B = 6

Length = 10m, Breadth = 6m

Verify:

Original area = 60

New area = (10+2)*(6-1) = 12*5 = 60