A field is in the form of a parallelogram, whose perimeter is 450 m and one of its sides is larger than the other by 75 m. Find the lengths of all sides.

Let us consider a parallelogram ABCD,

We know that the lengths of opposite sides of a parallelogram are equal.

i.e, AD = BC ...... (1)

AB = CD ...... (2)

We also know that Perimeter of Parallelogram is the sum of the lengths of its sides.

i.e, Perimeter of Parallelogram(P) = AB + BC + CD + DA - - (3)

According to the problem it is given that,

The perimeter of Parallelogram(P) is 450m and

One side is 75m larger than the other side.

Let us consider the length of smaller be ‘x’m

Then from the figure,

BC = AD = xm ...... - - (4)

Then, AB = CD = (x + 75)m ...... (5)

From eq(1),

⇒ x + x + 75 + x + x + 75 = 450 (since P = 450m)

⇒ 4x + 150 = 450

⇒ 4x = 450 - 150

⇒ 4x = 300

⇒

⇒ x = 75m.

From Eq(4) we can say that,

BC = DA = 75m.

AB = CD = (75 + 75) = 150m.

The lengths of sides AB, BC, CD and DA is 150m, 75m, 150m, 75m.