If the radius of a circle is diminished by 10%, then the area is diminished by:

Answer: Option C

Explanation:

Let the lengths of the line segments be x and x+2 cm
then,
$$\begin{aligned} {(x+2)}^2 - x^2 = 32 \\ x^2 + 4x + 4 - x^2 = 32 \\ 4x = 28 \\ x = 7 cm \end{aligned}$$

Answer: Option D

Explanation:

We know the product of diagonals is 1/2*(product of diagonals)

Let one diagonal be d1 and d2
So as per question

$$\begin{aligned} \frac{1}{2}*d1*d2 = 150 \\ \frac{1}{2}*10*d2 = 150 \\ d2 = \frac{150}{5} = 30 \\ \end{aligned}$$

Answer: Option C

Explanation:

$$\begin{aligned} \text{Area of triangle, A1 = }\frac{1}{2}*base*height \\ = \frac{1}{2}*15*12 = 90 cm^2 \\ \text{Area of second triangle =} 2*A1 \\ = 180 cm^2 \\ \frac{1}{2}*20*height = 180 \\ => height = 18 cm \end{aligned}$$

Answer: Option C

Explanation:

Let Breadth = x cm,
then, Length = 3x cm
$$\begin{aligned} x^2+{(3x)}^2 = {(8\sqrt{10})}^2 \\ => 10x^2 = 640 \\ => x = 8 \\ \end{aligned}$$
So, length = 24 cm and breadth = 8 cm
Perimeter = 2(l+b)
= 2(24+8) = 64 cm

Answer: Option A

Explanation:

Let the diagonals of the squares be 2x and 5x.
Then ratio of their areas will be
$$\begin{aligned} \text{Area of square} = \frac{1}{2}*{Diagonal}^2 \\ \frac{1}{2}*{2x}^2:\frac{1}{2}*{5x}^2 \\ 4x^2:25x^2 = 4:25 \end{aligned}$$