Question

1. Find the diameter of a circle when the circumference is 22 cm.
2. A gardener needs to fence n circular garden of radius 28 m. Find the
length of the fence required.
3. Find the base of a triangle whose height is 14cm/and area is 98 cm,
4. The area and length of a rectangle are 225 m2 and 17m respectively. Find
the breadth of rectangle.
5. What is the perimeter of n semloircle of radius 7 cm

6. How many times a runner has to run around a racing track 75m in
length and 25m in breadth in breadth to cover a distance of 800m?
7. A wire is in the shape of a rectangle of length 40cm and breadth 22cm. If
the same wire is again bent in the shape of a square, what will be the
measure of each side? Also find which shape encloses more aren?
8. The perimeter and area of a rectangle and area are equal. If the side of
the square is 8cm and length of rectangle is 12cm, find the brendth of
the rectangle.
9. The area of a right triangle is 24sq.cm. If one of the sides containing the
right angle is 8cm, find the length of its hypotenuse.


can anyone answer these qn​

Answer 1

Answer:

1. circumference=2 pie r

22=2×7÷22×r

22×7÷22×2=r

r=3.5

diameter = 2r

diameter = 7cm

Answer 2

1) Given: The circumference of circle is

22cm.

To find: The diameter of circle.

We know that,

Circumference = πd

Therefore,

πd=22

22/7*d =22

d/7 = 1

d = 7

So, the diameter of circle is 7cm.

2)Given: Radius of the garden is 28m.

To find: The length of fence required to

fence n circular gardens having radius 28m.

We know that circumference = 2πr

Therefore, circumference of n gardens

=2πrn

={2*22/7*28}n

={56*22/7}n

={8*22}n

={176}n

Thus, length of fence required to fence n gardens having radius 28m is (176*n) meters.

3) Given: Height of triangle is 14cm and area is 98cm.

To find: The length of base of triangle.

We know that,

Area of triangle = 1/2*base*height

or, 98 = 1/2*base*14

or, 98 = 7*base

or, base= 14

Therefore, the base of triangle is 14cm.

4) Given: The area of rectangle is 225m² and length of rectangle is 17m.

To find: The breadth of rectangle,

We know that,

Area of rectangle = length*breadth

or, 225 = 17*breadth

or, breadth = 13.235

Therefore, the breadth of the rectangle is 13.235m.

5) Given: Radius of semicircle is 7cm.

To find: Perimeter of n such semicircle.

We know that,

Perimeter of semicircle = πr, so,

Perimeter of n such semicircle = nπr

=n*22/7*7

=n*22

Therefore, perimeter of n semicircle is 22n(cm).

6) Given: length of track is 75m and breadth is 25m.

Now, since we need to know the number of times the runner needs to run around the track to cover 800m.

So, we need to find the perimeter of the track and then divide 800 with the perimeter.

Now, perimeter = 2(length+ breadth)

= 2(75+25)

=2*100

=200

So, we got the perimeter of track as 200m.

Now,

Total distance needed to cover = 800m

Therefore, no. of times runner needs to run across the track = 800/200

= 4

Therefore, the runner needs to run 4 times the rectangular track to cover the distance of 800m.

7) Given: When wire is in shape of rectangle, it's length is 40cm and breadth is 22cm.

To find: The measure of each side if the wire is bent in the shape of square.

Since, length of wire remain constant, therefore, the perimeter of rectangle and square will be same.

So,

2(length+ breadth) = 4*side or,

2(40+22) =4*side or,

62/2= side or,

Side = 31

Therefore, side of square will be 31cm.

Now to find which shape encloses more area,

Area of rectangle = length*breadth

= 40*22

= 880cm²

Area of square = side²

=31*31

=961cm²

So, we find that square encloses more area.

8) Given: Perimeter of rectangle is equal to area of square. Also, length of rectangle is 12cm and side of square is 8cm.

To find: The measure of breadth of rectangle.

Since, according to question,

2(length+breadth) = side²

2*(12+breadth) = 64

12 + breadth = 32

Breadth = 20

Therefore, the breadth of the rectangle is of 20 cm.

9) Given: The area of right triangle is 24cm². Also, the length of one side containing right angle is 8cm.

To find: The measure of Hypotenuse of triangle.

First, we need to find the other side,

We know that,

Area = 1/2*base*height or,

24=1/2*8*height

Height= 6cm.

Now, we have the measure of two sides of right triangle and we need to find the hypotenuse,

So, we use the Pythagorean theorem

Which is : base² + height² = hypotenuse²

8² + 6²=hypotenuse²

64 + 36 = hypotenuse²

Or, hypotenuse² = 100

Therefore, hypotenuse = 10

Therefore, the measure of hypotenuse is 10cm.