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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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2 years ago
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Which congruence theorem can be used to prove ABDA - ABDC?
oee [108]

Answer:

SAS(SIDE ANGLE SIDE)

Step-by-step explanation

AB side in ABDA = AB side in ABDC

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5 0
2 years ago
Shannon is selling boxes cookies and candy for a fundraiser. She's sold each box of cookies for $5.25. She also sold one one box
defon

Answer:

The minimum boxes of cookies is 39

Step-by-step explanation:

Let

x ----> the number of boxes of cookies sold

y ----> the number of boxes of candies sold

we know that

The word "at least" means "greater than or equal to"

so

The inequality that represent this problem is

5.25x+8.75y\geq 200

The solution is the shaded area above the solid line   5.25x+8.75y=200

using a graphing tool

The solution is the shaded area -----> see the attached figure

Find out the minimum boxes of cookies needed to sell to reach the goal

assuming only cookies are sold

For y=0

5.25x+8.75(0)\geq 200

5.25x\geq 200

solve for x

x\geq 38.1

Round up

therefore

The minimum boxes of cookies is 39

5 0
2 years ago
Solve right triangle ABC given the following: C = 90° , B = 53°, b = 23.
Anastasy [175]
A=17.33174
c=28.79912
A=37
area=199.31505


pls give brainliest if someone else comments :)
7 0
3 years ago
Me pueden ayudar en esto por favor​
Whitepunk [10]

Answer:

2cm: 6.28

4cm: 12.56

6cm: 18.84

8cm: 25.12

10cm: 31.4

12cm: 37.68

Step-by-step explanation:

3 0
3 years ago
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