Answer:
The perimeter of the rectangle = 18 cm
Step-by-step explanation:
* The figure consists of one rectangle and four squares
* Lets put the dimensions of the rectangle and the four squares
- The width of the rectangle is x
∵ The length of the rectangle is 5 cm longer than the width
∴ The length of the rectangle is x + 5
∵ Area the rectangle = L × W
∴ Area rectangle = x(x + 5) = x² + 5x ⇒ (1)
* There are four squares constructed each in one side
of the rectangle
- Two squares constructed on the length of the rectangle
∴ The length of the sides of the squares = x + 5
∵ Area the square = S²
∴ Its area = (x + 5)² ⇒ use the foil method
∴ Its area = x² + 10x + 25
∵ They are two squares
∴ Its area = 2x² + 20x + 50 ⇒ (2)
- Two squares constructed on the width of the rectangle
∴ The length of the sides of the squares = x
∴ Its area = x²
∵ They are two squares
∴ Its area = 2x² ⇒ (3)
- Area rectangle = x(x + 5) = x² + 5x ⇒ (3)
* Now lets make the equation of the area of the figure by
adding (1) , (2) and (3)
∴ The area of the figure = 2x² + 20x + 50 + 2x² + x² + 5x
= 5x² + 25x + 50⇒ (4)
∵ The area of the figure = 120 cm² ⇒ (5)
* Put (4) = (5)
∴ 5x² + 25x + 50 = 120 ⇒subtract 120 from both sides
∴ 5x² + 25x +50 - 120 = 0 ⇒ add the like term
∴ 5x² + 25x -70 = 0 ⇒ divide both sides by 5
∴ x² + 5x - 14 = 0 ⇒ factorize it to find the value of x
∴ (x - 2)(x + 7) = 0
* Lets equate each bracket by 0
∴ (x - 2) = 0 ⇒ x = 2
∴ (x + 7) = 0 ⇒ x = -7 ⇒ rejected no -ve side length
∴ x = 2
* Now lets find the dimensions of the rectangle
∵ Length rectangle = x + 5
∴ Length rectangle = 2 + 5 = 7 cm
∴ Width rectangle = 2
∵ The perimeter of the rectangle = 2(L + W)
∴ The perimeter of the rectangle = 2(2 + 7) = 18 cm
* The perimeter of the rectangle = 18 cm
