All categories

3 years ago

The perimeter of a triangle is 170 feet and the sides are in the ratio of 25:14:12. Find the area of the triangle.

1 answer:

6 0

Let
x,y, and z the long sides of the triangle

we know that

x+y+z=170 ft------> equation 1
x/y=25/14----> y=14x/25------> equation 2
y/z=14/12-----> equation 3
x/z=25/12----> z=12x/25------> equation 4

substitute equation 2 and equation 4 in equation 1
x+[14x/25]+[12x/25]=170------> multiply by 25 both sides
25x+14x+12x=4250
51x=4250
x=4250/51
x=250/3
y=14x/25------> y=(250/3)*(14/25)----> y=140/3
z=12y/14-----> (140/3)*12/14----> z=40

Using Heron's formula,
Area of the triangle = √s (s-a) (s-b) (s-c)
where s is the semiperimeter
s=170/2-----> s=85 ft
Area=√85*[85-250/3]*[85-140/3]*[85-40]
Area=9.22*[1.67]*[38.33]*[45]------> Area=26558.21 ft²

the answer is
26558.21 ft²

You might be interested in

Write the word sentence as an equation. Then solve the equation.

Nana76 [90]

Answer:

see below

Step-by-step explanation:

9 is the difference of a number n and 7.

Let's break this down.

"is" represents the equal sign.

"the difference" represents subtraction.

9 = n - 7

Now let's solve the equation.

9 = n - 7

Add 7 to both sides.

16 = n

Hope this helps!

7 0

2 years ago

Cheryl bought a sandwith or 5 1/2 dollars and a drink for $2.60 if she paid for her meal with $10 bill,how much money did she ha

QveST [7]

Answer:

$1.90

Step-by-step explanation:

8 0

2 years ago

Given the relationship x2 + 3y2 =12, with y > 0 and dx, dt = 2 units/min., find the value of dy, dt at the instant y = 1 unit

matrenka [14]

$\bf x^2+3y^2=12\implies \stackrel{chain~rule}{2x\cfrac{dx}{dt}}+3 \stackrel{chain~rule}{\left(2y\cfrac{dy}{dt}\right)}=0
\\\\\\
2x\cfrac{dx}{dt}+6y\cfrac{dy}{dt}=0
\implies 
6y\cfrac{dy}{dt}=-2x\cfrac{dx}{dt}\implies \cfrac{dy}{dt}=\cfrac{-2x\frac{dx}{dt}}{
6y\frac{dy}{dt}}
\\\\\\
\boxed{\cfrac{dy}{dt}=-\cfrac{x\frac{dx}{dt}}{3y}}\\\\
-------------------------------$

$\bf \textit{now, when y = 1, what is \underline{x}?}\qquad x^2+3y^2=12\implies x^2+3(1)^2=12
\\\\\\
x^2=9\implies x=\sqrt{9}\implies x=3\\\\
-------------------------------\\\\
\begin{cases}
y=1\\
x=3\\
\frac{dx}{dt}=2
\end{cases}\implies \cfrac{dy}{dt}=-\cfrac{3\cdot 2}{3\cdot 1}\implies \cfrac{dy}{dt}=-2$

7 0

2 years ago

which equation below represents the data in the table and PLEEEEASE show each and every step of how to solve I will make you the

kari74 [83]

The equation which represents the data in the table as in the task content is; Choice C; y = 2x +3.

<h3>What is the equation which represents the data in the table as attached?</h3>

It follows from the task content that the slope of the relation can be determined by means of the slope formula for a linear equation as follows;

Slope = (1-(-1))/(-1 -(-2))

Slope = 2.

Hence, the equation which represents the function is;

2 = (y-(-1))/(x -(-2))

2x + 4 = y +1

y = 2x + 3.

Therefore, the equation which represents the data in the table as in the task content is; Choice C; y = 2x +3.

Read more on equation of a table;

brainly.com/question/28028709

#SPJ1

8 0

1 year ago

Mark can remember only the first 4 digits of his friend's phone number. He also knows that the number has 7 digits and that the

denis-greek [22]

Answer:

<em>19800 seconds, or 330 minutes, or 5 hours + 30 minutes</em>

Step-by-step explanation:

<u>Number Permutations</u>

We know the phone number has 7 digits, 4 of which are known by Mark. This leaves him 3 digits to guess with. We also know the last one is not zero. The number can be represented as

XXY

Where X can be any digit from 0 to 9 and Y can be any digit from 1 to 9. The first two can be combined in 10x10 ways, and the last one can be of 9 ways, this gives us 10x10x9 = 900 possible permutations.

If each possible number takes him 22 seconds, every possibility will need

22x900=19800 seconds, or 330 minutes, or 5 hours + 30 minutes

3 0

2 years ago