Question

11.1 If the length of the square is x m then the total length of the field is
(d) (x + 4) m
(a) (2x + 3) m
(b) (3x + 3) m (c) (6x) m
11.2 What will be the perimeter of the whole figure in terms of x?
(a) 8x + 6
(b) 6x +6
(c) 3x + 3x
(d) 8x + 4
11.3 Find the value of x if the area of total field is 1260 m2
11.4 Find area of grassland and the flowerbed separately.
11.5 Find the ratio of area of grassland to area of flowerbed.​

Answer 1

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) .

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