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
jonny [76]
3 years ago
14

A rectangular parcel of land has an area of 6,000 ft2. A diagonal between opposite corners is measured to be 10 ft longer than o

ne side of the parcel. What are the dimensions of the land, correct to the nearest foot? ft (smaller value) by ft (larger value)
Mathematics
1 answer:
Drupady [299]3 years ago
3 0

Answer:

50ft by 120ft

Step-by-step explanation:

Area of a rectangle = L × W

6000ft² = L × W

L = 6000/W

When a diagonal line divides a rectangle into 2 right angled triangles, the diagonal line = Hypotenuse of either of the triangle and it is the longest side.

The formula for a right angle triangle =

a² + b² = c²( c = hypotenuse)

We are told in the question that:

A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel

Let us assume the side that the hypotenuse is longer than = Width

Hence, the Diagonal = (W + 10)²

Therefore

L² + W² = (W + 10)²

Since L = 6000/W

W² + (6000/W)² = (W + 10)²

W² + (6000/W)² = (W + 10) (W + 10)

W² + (6000/W)² = W² + 10W + 10W + 100

W² + (6000/W)² = W² + 20W + 100

W² - W² + (6000/W)² = 20W+ 100

6000²/W² = 20W + 100

6000² = W²( 20W + 100)

6000² = 20W³ + 100W²

20W³ + 100W² - 6000² = 0

20W³ + 100W² - 36000000 = 0

20(W³ + 5W² - 1800000) = 0

Factorising the quadratic equation,

20(W − 120)(W² + 125W + 15000) = 0

W - 120 = 0

W = 120

Therefore,

W(Width) = 120feet

Since the Width = 120 feet

We can find the length

6000ft² = L × W

L = 6000/W

L = 6000/120

L = 50 feet

The dimensions of the land, correct to the nearest foot is 50ft by 120ft

You might be interested in
<img src="https://tex.z-dn.net/?f=%5Ctext%7BI%20was%20eating%20cookies%20and%20had%20some%20thoughts.%20If%20I%20wanted%20to%20c
andrew-mc [135]

In the attachement, there is what I came up with so far. I think that finding 'a' is non-trivial, if possible at all.

A_c - the area of a circle

A_{cs} - the area of a circular segment

5 0
2 years ago
Which expression has a value of 15 when p=12
Arturiano [62]

Answer:

Please provide more information like answer choices, or even better a picture!

Step-by-step explanation:

If you'd like to add answer choices, you can simply type them in the comments below.

If you'd like to add a picture, you will have to make a new post.

Very sorry but it's not clear enough!

Hope this helps!

5 0
3 years ago
Read 2 more answers
Solve 4(x + 1) = 4x + 4<br><br> A- No solution<br> B- 0<br> C- All real numbers<br> D- 1
Tcecarenko [31]
The answer is: c- all real numbers
8 0
3 years ago
Solve for x. Would like if both could be answered if not just answer one.
ratelena [41]
328 is the answer sir
3 0
3 years ago
Read 2 more answers
A box contains 9 green marbles and 17 white marbles. If the first marble chosen was a white marble, what is the probability of c
pshichka [43]

Answer:

16/25

Step-by-step explanation:

Given

Number  of green marbles = 9

Number of White marbles = 17

Total number of marbles = 26

Probability of picking a white marble = 17/26

When a white marble is picked without replacement,

Probability of picking another white marble after first picking a white marble

= 16/25

= 0.64

This is because the total number of marbles would have reduced from 26 to 25 and the number of white marbles from 17 to 16.

4 0
3 years ago
Other questions:
  • Your bank balance is $102.35 and you've just made purchases for $20, $33.33, and $52.80. You then make deposits of $25 and $24.7
    6·2 answers
  • What is the cube root of 12? I have to show my work using common core.
    15·1 answer
  • A water storage tank is in the shape of a hemisphere (half a sphere) If the radius is 15 ft, approximate the volume of the tank
    13·1 answer
  • Henry decorated the top of each cupcake with 3 walnuts. If he has 56 walnuts, is that enough to decorate 2 dozen cupcakes? Expla
    13·2 answers
  • Barney has 16 2/3 feet of lumber that he is going to to cut into 4 equal pieces for a border on his garden. Which of the followi
    12·1 answer
  • Re-write this subtraction as an ADDITION of signed numbers. 3 − 7
    8·2 answers
  • The equation of the L, is y=5x+1
    11·1 answer
  • What is the area of a sector with a central angle of 255 and a radius of 18.4 m?
    8·1 answer
  • 1. Which equation represents the relationship shown in the table below? (1 point)
    14·1 answer
  • The bases on a softball field are square. What is the area of each base if one side is 15 inches? Do not write units.
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!