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ANEK [815]
3 years ago
6

What is the area of the largest rectangle that can be inscribed in an isosceles triangle with side lengths $8$, $\sqrt{80}$, and

$\sqrt{80}$? Assume that one side of the rectangle lies along the base of the triangle.

Mathematics
1 answer:
e-lub [12.9K]3 years ago
4 0
First let's solve the general case for an isosceles triangle of base 2 and height k. If the triangle is drawn so the base is on the x-axis and the apex is on the y-axis, the equation for the line containing the right side is
  y = -k(x-1)
Then a rectangle with x-dimension w will have an area that is the product of this width and the height y = -k((w/2)-1).
  area = w(-k(w/2 -1)) = (-k/2)w² +kw
The derivative of area with respect to w will be zero where the area is a maximum:
  d(area)/dw = 0 = -kw +k
  w = 1 . . . . . . add kw and divide by k
Using the formula for area, we find
  area = 1(-k(1/2-1)) = k/2
This value is 1/2 the total area of the triangle we started with.

If the side lengths of your triangle are 8, √80, and √80, the height will be given by the Pythagorean theorem as
  h = √((√80)² - (1/2·8)²) = √(80-16) = 8
Your triangle's area will be
  triangle area = (1/2)(8)(8) = 32

The maximum area of the inscribed rectangle will be half this value,
  16 square units

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A boat in still water is 32 mph. If the boat travels 72 miles upstream in the same time that it takes to travel 120 miles downst
dalvyx [7]
Dup= 72 miles 
<span>ddown= 120 miles </span>
<span>v= riverspeed </span>
<span>rup= 32mph - v </span>
<span>rdown= 32mph + v </span>
<span>t both ways= t </span>

<span>d=r*t </span>
<span>d/r=t </span>

<span>t=ddown/rdown </span>
<span>t=dup/rup </span>

<span>dup/rup = ddown/rdown </span>

<span>(72)/(32-v)=(120)/(32+v) </span>
<span>3840-120v=2304+72v </span>
<span>1536=192v </span>
<span>v=8</span>
8 0
2 years ago
PLEASE HELP I WILL GIVE BRAINLIEST
jok3333 [9.3K]

Answer:

x > 2

Step-by-step explanation:

Since the dot is not filled in, it does not include 2. Since it is moving to the right, it means it is more than 2.

Hope that helps!

7 0
3 years ago
Read 2 more answers
Molly has 1/2 cup of strawberries. She needs 3/8 cup of strawberries to make one batch of muffins. How many batches can she make
inn [45]

Answer:

1 and 1/8 of a batch

Step-by-step explanation:

First you multiply 1/2 by 4 and get for 8 and then you subtract 4/8 - 3/8 and you take the sum of that and add one hole

7 0
3 years ago
Can someone plz help me
JulsSmile [24]

Answer:

31.42

Step-by-step explanation:

7 0
2 years ago
❗ANSWER+EXPLANATION=100POINTS+BRAINLIEST❗<br>solve: (x+2)(5x-1)=0<br>thanks)​
IrinaVladis [17]

The solution to the given quadratic equation is;

x = -2 and x = 1/5

<h3>Roots of quadratic Equation </h3>

We are given the quadratic function;

(x + 2)(5x - 1) = 0

In quadratic functions, when it is expressed as;

(x + a)(x - b) = 0, what this means is that the factors of the quadratic equation or polynomial are; (x + a) and (x - b)

What that means is that the roots will be gotten from;

(x + a) = 0 and (x - b) = 0

Thus, applying the concept above on roots of a polynomial to our question, we have;

(x + 2) = 0 and 5x - 1 = 0

Solving them gives us;

x = -2 and x = 1/5

Read more on roots of quadratic equation at; brainly.com/question/8649555

4 0
2 years ago
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