Question

iii) The length of a rectangle is four times of its breadth. The perimeter of this rectangle in 1200 meter. The side of an another square is 70 meter. A new square is prepared whose area is equal to the sum of the area of these rectangle and square. Find the perimeter of the new square.​

Answer 1

Let :-

• Length of rectangle = 4x
• Breadth of rectangle = x

Given :-

• Perimeter of rectangle = 1200m
• The side of square = 70m

To Find :-

• The perimeter of new square = ?

Solution :-

To calculate the new perimeter of square at first we have to find the dimensions of rectangle and it's area after that we have to find out the area of square. At last we have to find the perimeter of new square by applying formula.

Calculation for rectangle :-

• Length = 4x Breadth = x

⟼ Perimeter of rectangle = 2(Length + Breadth)

⟼ 2(4x + x) = 1200

⟼ 5x = 600

⟼ x = 120m

Therefore, Length (4x) = 4 × 120 = 480m

Therefore, Breadth (x) = 1 × 120 = 120m

⟼ Area of rectangle = Length × Breadth

⟼ Area = 480 × 120

⟼ Area = 57600 m²

Calculation for square :-

• Side = 70m. Area = ?

⟼ Area of square = Side × Side

⟼ Area = 70 × 70

⟼ Area = 4900 m²

Calculation for new square :-

• Area of rectangle = 57600 m²
• Area of square = 4900 m²
• Let, side of the square be N

⟼ Area (new square) = Area (rectangle + square)

⟼ N × N = 57600 + 4900

⟼ N² = 62500

⟼ N = √62500

⟼ N = 250m

Therefore, the side of new square (N) = 250m

⟼ Perimeter of this square = 4 × Side

⟼ Perimeter = 4 × 250

⟼ Perimeter = 1000m

Hence, the perimeter of new square is 1000m.

Answer 2

Given :-

The length of a rectangle is four times its breadth. The perimeter of this rectangle is 1200 meters. The side of another square is 70 meters. A new square is prepared whose area is equal to the sum of the area of this rectangle and square.

To Find :-

The perimeter of the new square

Solution :-

①

Perimeter = 2(l + b)

Let the breadth be b and length be l

l = 4b (i)

1200 = 2(l + b)

1200/2 = l + b

600 = l + b (ii)

Putting the value of l in Eq. 2

600 = 4b + b

600 = 5b

600/5 = b

120 = b

Using 1

l = 4b

l = 4(120)

l = 480 m

②

Area of rectangle = length × breadth

Area = 480 × 120

Area = 57600 m²

③

Area of square = side²

Area = (70)²

Area = 4900 m²

④

Sum of the area of rectangle and square

4900 + 57600

62500

⑤

New area of the square = side × side

Let the side be s

Area = s × s

Area = s²

⑥

Sum of the area of rectangle and square = Area of new square

62500 = s²

√(62500) = s

250 = s

⑦

Perimeter of new square = 4 × s

Perimeter of new square = 4 × 250

Perimeter of new square = 1000 m