Question

a rectangle has an area of 105 CM square and perimeter 44cm determine the dimensions of the rectangle.

Answer 1

Let the Length of the Rectangle be : L cm

Let the Breadth of the Rectangle be : B cm

We know that Area of a Rectangle is given by : L × B

Given that the Area of Rectangle = 105 cm²

⇒ L × B = 105

We know that Perimeter of Rectangle is given by : 2(L + B)

Given that Perimeter of the Rectangle = 44 cm

⇒ 2(L + B) = 44

⇒ (L + B) = 22

⇒ L = 22 - B

Substituting L =  22 - B in L × B = 105 we get :

⇒ (22 - B) × B = 105

⇒ 22B - B² = 105

⇒ B² - 22B + 105 = 0

⇒ B² - 15B - 7B + 105 = 0

⇒ B(B - 15) - 7(B - 15) = 0

⇒ (B - 15)(B - 7) = 0

⇒ B = 15 or B = 7

Substituting the Breadth values in L = 22 - B we get :

If B = 15 then Length = 22 - 15 = 7

If B = 7 then Length = 22 - 7 = 15

So the Dimensions of the Rectangle can be (15 cm × 7 cm) or (7 cm × 15 cm)

Answer 2

I hope it clear to uu