1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
raketka [301]
3 years ago
8

The ratio of length and breadth of a rectangular playground is 3:2. There

Mathematics
1 answer:
Misha Larkins [42]3 years ago
7 0

Answer:

We know that the ratio of length and breadth of a rectangular playground is 3:2

Then if the length is L, and the breadth is B, we have the relationship:

L = (3/2)*B

Outside this playground, we have a jogging track of 2m, then if we also consider the jogging track the length and breadth are:

L' = L + 2m

B' = B + 2m

The area is the product between the area and the breadth, then the area is:

A = B'*L'

A = (L + 2m)*(B + 2m)

And remember that L = (3/2)*B

Then we get:

A =  ((3/2)*B + 2m)*(B + 2m)

And the area is 2816 m^2

Then we have:

A =  ((3/2)*B + 2m)*(B + 2m) = 2816 m^2

Now we can solve the equation:

((3/2)*B + 2m)*(B + 2m) = 2816 m^2

(3/2)*B^2 + 3m*B + 2m*B + 4m^2 = 2816 m^2

(3/2)*B^2 + 5m*B =  2816 m^2 - 4m^2 = 2812m^2

Then we can write:

(3/2)*B^2 + 5m*B -  2812m^2 = 0

We can solve this if we use Bhaskara's formula:

B = \frac{-(5m) +- \sqrt{(5m)^2 - 4*(3/2)*(-2812m^2)} }{2*(3/2)} = \frac{-5m +-130m}{3}

One solution is negative, so we can discard that one, then we only take the positive:

B = (-5m + 130m)/3 = 41.67m

And L = (3/2)*B

L = (3/2)*40.7m = 62.5m

The breadth is 41.67 meters and the length is 62.5 meters.

You might be interested in
What is the equation of the circle whose diameter has endpoints (8,-2) and (-2,6)?
klemol [59]

Answer:

(x-3)^{2} +(y-2)^{2}=41

Step-by-step explanation:

step 1

Find the diameter of the circle

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

we have

A(8,-2)\\E(-2,6)  

substitute the values

d=\sqrt{(6+2)^{2}+(-2-8)^{2}}

d=\sqrt{(8)^{2}+(-10)^{2}}

d=\sqrt{164}\ units

d=2\sqrt{41}\ units

step 2

Find the center of the circle

The center is the midpoint of the diameter

The center is equal to

C=(\frac{8-2}{2},\frac{-2+6}{2})

C=(3,2)

step 3

Find the equation of the circle

The equation of the circle in center radius form is equal to

(x-h)^{2} +(y-k)^{2}=r^{2}

we have

(h,k)=(3,2)

r=2\sqrt{41}/2=\sqrt{41}\ units ---> the radius is half the diameter

substitute

(x-3)^{2} +(y-2)^{2}=(\sqrt{41})^{2}

(x-3)^{2} +(y-2)^{2}=41

4 0
4 years ago
An internet service provider uses the function R = 3 log(a + 2) + 15 to relate R, the sales revenue from hosting websites, to a,
elena55 [62]

Answer:

a=10R−153−2

Step-by-step explanation:

3 0
3 years ago
Ok this is a long one, so any help would mean the world, even if you only do part of it.
jeka94
It’s shehshdhshhshshshhs
8 0
3 years ago
Convert the decimal to a fraction in simplest form. 0.25 =
Yuliya22 [10]
The answer in simplest form is 1/4.
4 0
3 years ago
Read 2 more answers
1+√3+1-√3<br>1 * 604 * 909 ​
brilliants [131]

1 + √3 + 1 - √3

= 1 + 1

= <u>0</u>

1 * 604 * 909

= <u>549,036</u>

6 0
3 years ago
Read 2 more answers
Other questions:
  • A model of a boat is 6 inches long. If the scale is 1/3 of an inch to one foot, what is the actual length of the boat?
    12·2 answers
  • Solve 12 – (2 × 3)a.6b.12c.12(2)d. 2 to the 3rd power
    7·1 answer
  • PLEASE HELP ASAP!!! :)<br><br>Look AT THE PICTURE PLS HURRY
    14·1 answer
  • the vertex angle of on isosceles triangle measures 42 a base angle in the triangle has a measure given by 2x+3
    11·1 answer
  • What is the answer for 39 40 36 37 33 34
    8·2 answers
  • D. Lamar's teacher extended the graph as shown below and asked Lamar to write the function for the graph shown below using f(x)
    9·1 answer
  • Calaveras county in California imposes a 7.25% sales tax on goods purchased in that county. How much tax is imposed on a $56.96
    5·1 answer
  • The least common multiple of two numbers is 40. The difference of the two numbers is 2. What are the numbers?
    9·1 answer
  • Faye has a drink with 120 milligrams of caffeine. Each hour, the amount of caffeine in her body will be 80% of the amount from t
    8·2 answers
  • Simplify the number into simplest radical form. Use the factor tree to help determine the factors. StartRoot 96 Endroot StartRoo
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!