Question

The length of a rectangular farm is (2x + 5) m and its width is (x+4) m. The perimeter of the farm is 102 m.

Answer 1

{correct question}

Question : The length of a rectangular farm is (2x + 5) m and its width is (x+4) m. The perimeter of the farm is 102 m. Find the length and the breadth and area of the rectangular farm.

Solution :

➜ Length of farm = (2x + 5) m ----{1}

➜ Breadth of farm = (x + 4) m ----{2}

➜ Area of farm = 102 m ----{3}

Now, by formula of perimeter of rectangle;

➜ Per =2 * {length + breadth}

➜ 102 = 2 * {(2x + 5) + (x + 4)}

➜ 102 = 2 * {2x + 5 + x + 4}

➜ 102 = 2 * {2x + x + 5 + 4}

➜ 102 = 2 * {3x + 9}

➜ 102 = 6x + 18

➜ 6x = 102 - 18

➜ 6x = 84

➜ x = 84/6

➜ x = 14

Now, put value of x in eq. {1} and eq. {2}

➜ Length of farm = (2x + 5) m

➜ Length of farm = (2 * 14 + 5) m

➜ Length of farm = (28 + 5) m

➜ Length of farm = 33 m and

➜ Breadth of farm = (x + 4) m

➜ Breadth of farm = (14 + 4) m

➜ Breadth of farm = 18 m

Now, by formula area of rectangle;

➜ Area of farm = Length * breadth

➜ Area of farm = 33 * 18

➜ Area of farm = 594 m²

Answer : Hence, the length and the breadth of the rectangular farm are 33 m and 14 m respectively. And the area of the farm is 594 m².