The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares .

Answer: Option D

Explanation:

If area is given then we can easily find side of a square as,
$$\begin{aligned}Side = \sqrt{69696} \\ = 264 cm \\ \text{we know diagonal =}\sqrt{2}\times side \\ = \sqrt{2}\times 264 \\ = 1.414 \times 264 \\ = 373.296 cm \end{aligned}$$

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 D

Explanation:

Let original length = x
and original width = y
Decrease in area will be
$$\begin{aligned} = xy-\left( \frac{80x}{100}\times\frac{90y}{100}\right) \\ = \left(xy- \frac{18}{25}xy\right) \\ = \frac{7}{25}xy \\ \text{Decrease = }\left(\frac{7xy}{25xy} \times100\right) \% \\ = 28\% \end{aligned}$$

Answer: Option A

Explanation:

We are given with length and area, so we can find the breadth.
as Length * Breadth = Area
=> 20 * Breadth = 680
=> Breadth = 34 feet

Area to be fenced = 2B + L = 2*34 + 20
= 88 feet

Answer: Option C

Explanation:

Question seems to be typical, but trust me it is too easy to solve, before solving this, lets analyse how we can solve this.
We are having speed and time so we can calculate the distance or perimeter in this question.
Then by applying the formula of perimeter of rectangle we can get value of length and breadth, So finally can get the area. Lets solve it:

Perimeter = Distance travelled in 8 minutes,
=> Perimeter = 12000/60 * 8 = 1600 meter. [because Distance = Speed * Time]

As per question length is 3x and width is 2x
We know perimeter of rectangle is 2(L+B)
So, 2(3x+2x) = 1600
=> x = 160
So Length = 160*3 = 480 meter
and Width = 160*2 = 320 meter

Finally, Area = length * breadth
= 480 * 320 = 153600