The length of a rectangle is three times of its width. If the length of the diagonal is $$\begin{aligned}8\sqrt{10}\end{aligned}$$ , then find the perimeter of the rectangle.

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 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 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

Answer: Option C

Explanation:

$$\begin{aligned} \text{We know area of square =}a^2 \\ \text{Area of triangle =}\frac{1}{2}*a*h \\ => \frac{1}{2}*a*h = a^2 \\ => h = 2a \end{aligned}$$

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