Question

Find the sides of a rectangle whose perimeter is 100m and area 600 sq.m

Answer 1

Given :

⠀⠀⠀⠀⠀• perimeter of rectangle = 100 m

⠀⠀⠀⠀⠀• area of rectangle = 600 m²

⠀⠀⠀⠀⠀⠀⠀⠀⠀

To Find :

⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀• Sides of reactangle

⠀

Solution :

⠀⠀⠀⠀⠀•Let 'x' be the length of rectangle

⠀⠀⠀⠀and 'y' be the breadth of rectangle.

⟹ Perimeter of rectangle = 2 ( L + B )

⟹ Perimeter of rectangle = 2( x + y )

⟹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀100 = 2x + 2y⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀...equation(1)

⟹ Area of rectangle = L × B

⟹ Area of rectangle = xy

⟹ ⠀⠀⠀⠀⠀⠀⠀⠀600 = xy

⟹ ⠀⠀⠀⠀⠀⠀⠀⠀600 = x⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀y

⠀⠀⠀

substituting x = 600/y in equation( 1 )

⟹ ⠀⠀⠀⠀2x + 2y = 100

⟹⠀⠀⠀ 2×600 + 2y = 100

⠀⠀⠀⠀⠀⠀⠀y

⟹⠀⠀⠀⠀1200 + 2y² = 100y

⟹⠀⠀⠀⠀y² -50y +600 =0

⟹⠀⠀⠀⠀y² -30y -20y + 600 = 0

⟹⠀⠀⠀⠀y(y -30) -20(y -30) = 0

⟹⠀⠀⠀⠀(y -20) =0 or ( y -30) = 0

⟹⠀⠀⠀⠀y = 20 or y = 30

Substituting (y = 20) in equation (1)

⟹⠀⠀⠀⠀2x + 2y = 100

⟹⠀⠀⠀⠀2x + 40 = 100

⟹⠀⠀⠀⠀x = 30

$\mathbb{ANSWER}$

The sides of the given rectangle are 30 cm and 20 cm.

Answer 2

$hello$

The sides of the given rectangle is 30cm and 20cm.