Question Detail

What will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of the rectangle as base and a vertex on the opposite side of the rectangle ?

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 :)

1. A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m , then the altitude of the triangle is.

200 m
150 m
148 m
140 m

Answer: Option A

Explanation:

Let the triangle and parallelogram have common base b,
let the Altitude of triangle is h1 and of parallelogram is h2(which is equal to 100 m), then

$\begin{aligned} \text{Area of triangle =}\frac{1}{2}*b*h1\\ \text{Area of rectangle =}b*h2\\ \text{As per question }\\ \frac{1}{2}*b*h1 = b*h2 \\ \frac{1}{2}*b*h1 = b*100 \\ h1 = 100*2 = 200 m \\ \end{aligned}$

2. If the ratio of the areas of two squares is 225:256, then the ratio of their perimeters is :

15:12
15:14
15:16
15:22

Answer: Option C

Explanation:

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

3. Find the circumference of a circle, whose area is 24.64 meter sqaure

17.90m
17.80m
17.60m
17.40m

Answer: Option C

Explanation:

$\begin{aligned} \text{Area of Square =} \pi*r^2\\ => \pi*r^2 = 24.64 \\ => r^2 = \frac{24.64}{22}*7 \\ => r^2 = 7.84 \\ => r = \sqrt{7.84} \\ => r = 2.8 \\ \text{Circumference =}2\pi*r\\ = 2*\frac{22}{7}*2.8 \\ = 17.60m \end{aligned}$

4. 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 .

22 cm
24 cm
26 cm
28 cm

Answer: Option B

Explanation:

We know perimeter of square = 4(side)
So Side of first square = 40/4 = 10 cm
Side of second square = 32/4 = 8 cm

Area of third Square = 10*10 - 8*8
= 36 cm

So side of third square = 6 [because area of square = side*side]
Perimeter = 4*Side = 4*6 = 24 cm

5. 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.

60 cm
62 cm
64 cm
66 cm

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

Question Detail

What will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of the rectangle as base and a vertex on the opposite side of the rectangle ?

1. A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m , then the altitude of the triangle is.

2. If the ratio of the areas of two squares is 225:256, then the ratio of their perimeters is :

3. Find the circumference of a circle, whose area is 24.64 meter sqaure

4. 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 .

5. 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.

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Question Detail

What will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of the rectangle as base and a vertex on the opposite side of the rectangle ?

1. A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m , then the altitude of the triangle is.

2. If the ratio of the areas of two squares is 225:256, then the ratio of their perimeters is :

3. Find the circumference of a circle, whose area is 24.64 meter sqaure

4. 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 .

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

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5. 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.