Ravi has a field with a flowerbed and grass land. The grass land is in
the shape of rectangle while flowerbed is in the shape of square. As
shown in figure.The length of the grassland is found to be 3 m more
than twice the length of the flowerbed. 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
Answers
Answer:
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Answer:
(i) Option (b)
(ii) Option (a)
(iii) Option (c)
(iv) Option (a)
Step-by-step explanation:
(i) Given: The length of square is x m. Also, rectangle is found to be 3 m more than twice the side of the square.
⇒ Length of rectangle = (2x+3) m
⇒ Total length of the field = Length of rectangle + Side of square
or Total length of the field = 2x + 3 + x
or Total length of the field = (3x+3) m
(ii) Perimeter of figure = 2(Total length of field) + 2(Side of square)
⇒ Perimeter of figure = 2(3x+3) + 2x
⇒ Perimeter of figure = 6x+6+2x
⇒ Perimeter of figure = (8x+6) m
(iii) Area of field = (Total length of field)×(Side of square) = 1260 m²
⇒ (3x+3).x = 1260
or 3(x²+x) = 1260
or x²+x = 420
or x²+x-420 = 0
or x²+21x-20x-420 = 0
or x(x+21)-20(x+21) = 0
or (x+21)(x-20) = 0
⇒ x = 20m {∵Length cannot be negative}
(iv) Now, length of rectangle = 2x+3 = 2×20+3 = 43 m
And, side of square = x = 20 m
⇒Area of grassland (rectangle) = length×breadth = 43×20
⇒Area of grassland (rectangle) = 860 m²
Also, area of flowerbed (square) = (side)² = 20²
⇒Area of flowerbed (square) = 400 m²
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