a rectangular garden has an area of 84 m² and a perimeter of 38 m. Find the dimension of the rectangular garden.
Answers
Answer:
Let the Length of the garden be 'l' and width be 'w.'
- Area of rectangular garden = 84 m²
- Perimeter of rectangular garden = 38 m
Unknown = Dimensions of the rectangular garden.
❍ According to Question now :
➝ Area of rectangle = Length × Width
➝ 84 = l × w ........[Equation I]
→ Perimeter of reactangle = 2 (Length + Width)
→ 38 = 2 (Length + Width)
→ 38 = 2 (l + w)
Now, Divide both sides by 2
→ 19 = l + w
→ l = 19 - w .......[Equation II]
Substituting value of l = 19 - w in equation (I) :
᠉ 84 = l × w
᠉ 84 = (19 - w) w
᠉ 84 = 19w - w²
᠉ w² - 19w + 84 = 0
Now, by Using splitting middle term we get :
᠉ w² - 12w + 7w + 84 = 0
᠉ w(w - 12) - 7(w - 12) = 0
᠉ (w - 12) (w - 7) = 0
᠉ w = 12 or 7
Now Substituting w = 12 in equation (II) :
᠉ l = 19 - w
᠉ l = 19 - 12
᠉ l = 7 m
As we know that length is always greater than width Therefore this is not required solution.
Now Substituting w = 7 in equation (II) we get :
᠉ l = 19 - w
᠉ l = 19 - 7
᠉ l = 12 m
Therefore,
- Length of rectangular garden = 12 m
- Width of rectangular garden = 7 m