ZS Associates Geometry Quiz-1

Area of the rectangle = 40 \times 25 = 1000 sq. m
Cost to cover the rectangle with grass bed = 1000 \times 35 = Rs. 35000

The base of the triangle = 15 cm
Area of the triangle = 225 sq. cm
Area of a right angled triangle = \frac{1}{2}\times Base \times height
225= 15 x height
Height = 15 cm.

Let the radius of the larger circle be r_{1} cm and the radius of the smaller circle be r_{2} cm.
According to the question ,
2\pi r_{1} - 2\pi r_{2} = 190
2\pi r_{1} - 2\times 3.14\times 10 = 190
2\pi r_{1} = 190 + 62.83
2\pi r_{1} = 252.8
r_{1} = 40.23 cm
Thus, the radius of the largest circle is 40.23 cm.

Let the length be 2x and width be 3x units respectively.
Taking this, Perimeter = 2\times \left ( 2x +3x\right ) = 10x
Area = 2x\times 3x = 6x^{2}
Let the Perimeter be m units and area be 4m sq. units respectively.
According to the ques,
Perimeter x 4 = Area
Area = 4\times 10x = 40x sq. units
40x = 6x^{2}
x = \frac{40}{6}
x = 6.66 units
Length of the garden = 2\times 6.66 = 13.32 units.

Let x and y be the length and breadth of the rectangle respectively.
Then, x - 4 = y + 3 or x - y = 7.
Area of the rectangle = xy; area of the square = (x - 4) (y + 3)
So, (x - 4) (y + 3) = xy ⇔ 3x – 4y = 12
Solving (i) and (ii), we get x = 16 and y = 9.
So, the perimeter of the rectangle = 2(x + y) ⇒ [2 (16 + 9)] cm = 50 cm.

(L+B)^{2} = (L-B)^{2} +4 LB
= (L+B)^{2} = (8)^{2} +4\times 9
On solving, we get, L+B = 10
And, perimeter of a rectangle = 2\times(L+B)
Hence, perimeter = 20 cm

Here it is not possible to find the circumference as there are two unknowns in the problem i.e breadth and radius. Thus option (d).

(L+B)^{2} = (L-B)^{2} +4 LB
= (L+B)^{2}= (6)^{2} +4\times 16
On solving, we get, L+B = 10
And, perimeter of a rectangle = 2(L+B)
Hence, perimeter = 20 m

Let the diagonals of the squares be 2x and 5x respectively.
So, the ratio of their areas =
\frac{1}{2}\times (2x)^2 : \frac{1}{2}\times (5x)^2
⇒4x² : 25x² ⇒ 4 : 25.

Let the edge of the cube be a. Then,
\therefore \sqrt{3}a = 6\sqrt{3} \Rightarrow a = 6
So, Volume = a^{3} = (6 \times 6 \times 6) cm^{3} ⇒ 216 cm^{3}.
Surface area = 6a^{2} ⇒ (6 \times 6 \times 6) cm^{2} ⇒ 216 cm^{2}.