One side of rectangular field is 15 meter and one of its diagonals is 17 meter. Then find the area of the field.

Answer: Option C

Explanation:

$$\begin{aligned} \text{Number of bricks =}\frac{\text{Courtyard area}}{\text{1 brick area}} \\ = \left( \frac{2500 \times 1600}{20 \times 10} \right) \\ = 20000 \end{aligned}$$

Answer: Option D

Explanation:

As far as questions of Area or Volume and Surface area are concerned, it is all about formulas and very little logic. So its a sincere advice to get all formulas remembered before solving these questions.

Lets solve this,

$$\begin{aligned} \text{Area of rectangle =}l*b\\ \text{Area of triangle =}\frac{1}{2}l*b\\ \text{Ratio =}l*b:\frac{1}{2}l*b \\ = 1:\frac{1}{2} \\ = 2:1 \end{aligned}$$

One little thing which should be taken care in this type of question is, be sure you are calculating ration in the given order of the question.
If it is ratio of triangle and rectangle then we have to write triangle formula first. cheers :)

Answer: Option B

Explanation:

Let breadth =x metres.
Then length =(115x/100)metres.
$$\begin{aligned} =x*\frac{115x}{100}= 460\\ x^2=(460 x 100/115) \\ x^2=400 \\ x= 20 \\ \end{aligned}$$

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:

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