Ravi has a field with a flowerbed and grass land. The grassland is in
the shape of a rectangle while flowerbed is in the shape of a square. As
shown in figure. The length of the grassland is found to be 3 m more
than twice the length of the flowerbed. The total area of the whole land
is 1260 m 2
.
i) If the length of the square is x m then the total length of the field is
(a) (2x + 3) m (b) (3x + 3) m (c) (6x) m (d) ( x + 4) m
ii) What will be the perimeter of the whole figure in terms of x?
(a) 8x + 6 (b) 6x +6 (c) 3x2+ 3x (d) 8x + 4
iii) Find the value of x if the area of total field is 1260 m2
.
(a)30 m (b) 40 m (c) 20 m (d) none
iv) Find area of grassland and the flowerbed separately.
(a)860 m2
,400 m2 (b) 900 m2
,360 m2
(c) 1000 m2
,260 m2
(d) none
Please not for free points
Answers
Answer:
i). Finding the total length of the field:
If the length of the square flowerbed = "x" m
Then, according to the question,
The length of the rectangle grassland = "2x + 3" m
∴ The total length of the field is,
= [Length of the grassland] + [length of the flowerbed]
= (2x + 3) + x
= (3x + 3) m
Thus, the total length of the field is → option (b) → (3x + 3) m
(ii). Finding the perimeter of the whole figure:
∴ The perimeter of the whole figure is,
= sum of all sides of the whole figure
= (2x + 3) + x + x + x + (2x + 3) + x
= (8x + 6) m
Thus, the perimeter of the whole field is → option (a) → (8x + 6) m
(iii). Finding the value of x:
The total area of the field = 1260 m² (given)
i.e., [Area of the rectangle grassland] + [Area of the square flowerbed] = 1260
∴ [(2x + 3)\times x] + [x^2] = 1260[(2x+3)×x]+[x
2
]=1260
\implies 2x^2 + 3x + x^2 = 1260⟹2x
2
+3x+x
2
=1260
\implies 3x^2 + 3x - 1260 = 0⟹3x
2
+3x−1260=0
dividing by 3 throughout
\implies x^2 + x - 420 = 0⟹x
2
+x−420=0
\implies x^2 + 21x - 20x - 420 = 0⟹x
2
+21x−20x−420=0
\implies x(x + 21) - 20(x + 21) = 0⟹x(x+21)−20(x+21)=0
\implies (x+21)(x-20)=0⟹(x+21)(x−20)=0
\implies x = -21 \:or\: 20⟹x=−21or20
since x represents the side of the square flowerbed and side cannot be in negative
∴ \bold{x = 20}x=20
Thus, the value of x is → 20 m.
(iv). Finding the area of the grassland and flowerbed separately:
∴ Area of the rectangular grassland is,
= length × breadth
= (2x + 3) \times x(2x+3)×x
substituting the value of x = 20 from (iii)
= \{(2\times 20)+3\} \times 20{(2×20)+3}×20
= \{40+3\} \times 20{40+3}×20
= 43\times 2043×20
= \bold{860\:m^2}860m
2
∴ Area of the square flowerbed is,
= side²
= x^2x
2
substituting the value of x = 20 from (iii)
= (20)^2(20)
2
= \bold{400\:m^2}400m
2
Thus, the area of grassland and the flowerbed separately is → option (a) → 860 m² and 400 m² respectively.
Question :- Ravi has a field with a flowerbed and grass land. The grassland is in the shape of a rectangle while flowerbed is in the shape of a square. As shown in figure. The length of the grassland is found to be 3 m more than twice the length of the flowerbed. The total area of the whole land is 1260 m² .
i) If the length of the square is x m then the total length of the field is
(a) (2x + 3) m (b) (3x + 3) m (c) (6x) m (d) ( x + 4) m
ii) What will be the perimeter of the whole figure in terms of x ?
(a) 8x + 6 (b) 6x +6 (c) 3x2+ 3x (d) 8x + 4
iii) Find the value of x if the area of total field is 1260².
(a)30 m (b) 40 m (c) 20 m (d) none
iv) Find area of grassland and the flowerbed separately.
Solution :-
given ,
→ Length of grassland(Rectangle) = 2 * Length of flowerbed(square) + 3 .
so,
→ Length of grassland = 2 * x + 3 = (2x + 3) m .
then,
= Length of the field = Length of grassland + Length of flowerbed = (2x + 3) + x = (3x + 3) m. (b) (Ans.i)
now,
→ Perimeter of the whole figure = 2(Length of grassland) + 2(Length of flowerbed) = 2(2x + 3) + 2*x = 4x + 6 + 2x = (8x + 6) m. (a) (Ans.ii)
now,
→ Area of grassland + Area of flowerbed = 1260 m².
→ x(2x + 3) + (x)² = 1260
→ 2x² + 3x + x² = 1260
→ 3x² + 3x = 1260
→ 3(x² + x - 420) = 0
→ x² + x - 420 = 0
→ x² + 21x - 20x - 420 = 0
→ x(x + 21) - 20(x + 21) = 0
→ (x + 21)(x - 20) = 0
→ x = 20 or (-21) .
since sides cant be in negative. Therefore, value of x is 20m. (c) (Ans.iii)
then,
→ Area of grassland = L * B = (2x + 3) * x = (2*20 + 3) * 20 = (40 + 3) * 20 = 43 * 20 = 860 m². (Ans.iv)
and,
→ Area of flowerbed = (side)² = (x)² = (20)² = 400 m². (Ans.iv) .
Learn more :-
! Read the Source/Text given below and answer four questions:
Veena planned to make a jewellery box to gift her friend ...
https://brainly.in/question/33406193
4. An architect is a skilled professional who plans and designs buildings and generally plays a key
role in their constr...
https://brainly.in/question/36748376