What will be the cost of gardening 1 meter boundary around a rectangular plot having perimeter of 340 meters at the rate of Rs. 10 per square meter ?

Answer: Option D

Explanation:

$$\begin{aligned} l*b = 460 m^2 \end{aligned}$$ .. (i)
Lets suppose breadth of plot is = b rnLength will be, $$\begin{aligned}l=b*\frac{100+15}{100}\\=\frac{115b}{100}\end{aligned}$$ .. (ii)

From (i) and (ii), we get :
$$\begin{aligned} \frac{115b}{100}*b = 460 \\ b^2 = \frac{46000}{115} = 400 \\ => b = \sqrt{400} = 20 meter \end{aligned}$$

Answer: Option A

Explanation:

$$\begin{aligned} \text{We know }h^2 = b^2+h^2 \\ =>\text{Other side }= \sqrt{(17)^2-(15)^2} \\ = \sqrt{289-225} = \sqrt{64} \\ = 8 meter \\ Area = Length \times Breadth \\ = 15\times8 m^2 = 120 m^2 \end{aligned}$$

Answer: Option C

Explanation:

$$\begin{aligned} \frac{a^2}{b^2} = \frac{225}{256} \\ \frac{15}{16} \\ <=> \frac{4a}{4b} = \frac{4*15}{4*16} \\ = \frac{15}{16} = 15:16 \end{aligned}$$

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 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,

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