The area of a square is 69696 cm square. What will be its diagonal ?

Answer: Option A

Explanation:

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

Answer: Option B

Explanation:

In this question, we are having perimeter.
We know Perimeter = 2(l+b), right
So,
2(l+b) = 340
As we have to make 1 meter boundary around this, so
Area of boundary = ((l+2)+(b+2)-lb)
= 2(l+b)+4 = 340+4 = 344

So required cost will be = 344 * 10 = 3440

Answer: Option A

Explanation:

Clearly first we need to find the areas of the given squares, for that we need its side.

Side of sqaure = Perimeter/4

So sides are,

$$\begin{aligned} \left(\frac{24}{4}\right),\left(\frac{32}{4}\right),\left(\frac{40}{4}\right),\left(\frac{76}{4}\right),\left(\frac{80}{4}\right) \\ = 6,8,10,19,20 \\ \text{Area of new square will be }\\ = [6^2+8^2+10^2+19^2+20^2] \\ = 36+64+100+361+400 \\ = 961 cm^2 \\ \text{Side of new Sqaure =}\sqrt{961} \\ = 31 cm \\ \text{Required perimeter =}(4\times31) \\ = 124 cm \end{aligned}$$

Answer: Option A

Explanation:

$$\begin{aligned} \text{Ratio of sides =}\frac{1}{2}:\frac{1}{3}:\frac{1}{4} \\ =6:4:3\\ Perimeter = 52 cm \\ \text{So sides are =} \\ \left( 52*\frac{6}{13}\right)cm,\left( 52*\frac{4}{13}\right)cm, \left( 52*\frac{3}{13}\right)cm \end{aligned}$$
a = 24 cm, b = 16 cm and c = 12 cm
Length of the smallest side = 12 cm

Answer: Option A

Explanation:

$$\begin{aligned} 2\pi R1 = 4 \pi \\ => R1 = 2 \\ 2\pi R2 = 8 \pi \\ => R2 = 4 \\ \text{Original Area =} 4\pi * 2^2 \\ = 16 \pi \\ \text{New Area =} 4\pi * 4^2 \\ = 64 \pi \end{aligned}$$

So the area quadruples.