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
Gnesinka [82]
3 years ago
10

[4] what is the largest possible area for a right triangle whose hypotenuse is 5cm long, and what are its dimensions? 25

Mathematics
1 answer:
maria [59]3 years ago
4 0
Let the base and height of the right triangle be b and h respectively.

Then the area of the triangle (which is to be maximized) is

A = bh/2.  Draw the triangle with the right angle positioned at the origin, in the first quadrant.

We are told that the hypotenuse is 5 cm.  Then 

b^2 + h^2 = 25 cm^2 must be true.  Alternatively, b = sqrt(25-h^2).

We want to meximize the area of this triangle.  In other words, maximize

A = (b)(h)/2, or, equivalently, maximize A = [sqrt(25-h^2)](h)/2.

Maximize A by differentiating the above formula for A with respect to h and finding the critical value for h.  Once you have that h value, calculate the corresponding b value and find the max area via    A = bh/2.

You might be interested in
What times what equals 64
vova2212 [387]
Possible answers...

64*1=64

32*2=64

4*16=64

8*8=64
5 0
3 years ago
Candidate C received 15,000 fewer votes than candidate B. If a total of 109,000 votes were cast, how many votes did candidate B
Zina [86]

Answer: Candidate B has 69,500 votes!

Step-by-step explanation:

one easy way to solve this is by dividing 109,000 in half and that gives us

54500 and 54500 but since Candidate C has 15000 less

we subtract 15000 from candidate c and add 15000 from candidate b

which gives us

Candidate C= 39,500 votes

Candidate B= 69,500 votes

please give brainliest!

7 0
3 years ago
What are all of the real roots of the following polynomial? f(x) = x4 - 13x2 + 36
GREYUIT [131]
ANSWER

A. -3, -2, 2, and 3

EXPLANATION

The given polynomial function is,

f(x) = {x}^{4} - 13 {x}^{2} + 36

To find the real roots, we equate the function to zero to obtain;

{x}^{4} - 13 {x}^{2} + 36 = 0

We can solve this equation as a quadratic equation in
{x}^{2}.

Thus we rewrite the equation as,

({x}^{2})^{2} - 13 {x}^{2} + 36 = 0

We split the middle term to get,

({x}^{2})^{2} - 9 {x}^{2} - 4 {x}^{2} + 36 = 0.

We factor to get,

{x}^{2} ( {x}^{2} - 9) - 4( {x}^{2} - 9) = 0

We factor to get,

( {x}^{2} - 9)( {x}^{2} - 4) = 0

Either

{x}^{2} - 9 = 0
or

{x}^{2} - 4 = 0

x = \pm \sqrt{9} \: or \: x = \pm \sqrt{4}
x = \pm3 \: or \: x = \pm2

x=-3,-2,2,3

The correct answer is A
5 0
3 years ago
Read 2 more answers
15 POINTS can someone please help me with this?
jarptica [38.1K]
X=55 Explanation: the square is a right angle symbol and that means the angle is 90 degrees so just subtract 35 from the 90 to get x
8 0
3 years ago
Arthur is building a rectangular sandbox for his son. The area of the sandbox is 17 23/32 square feet. If the length of the sand
Elina [12.6K]
Author is building a regular sandbox for his son, the area of the sandbox is 17 23/32 square ft. If the length of if the length of the sandbox is 3 3/8 ft
5 0
3 years ago
Read 2 more answers
Other questions:
  • How to do for these questions? Help! Thanks :) ​
    5·1 answer
  • What is the answer to 16b+5c-10-8c+2b
    8·1 answer
  • the area of a rectangular field is 8148 yards squared if the width of the field is 84 yards what is its length
    6·1 answer
  • What is the sum of 3/8 and 1/6?
    5·2 answers
  • What is the negative square root of 64/4?
    6·1 answer
  • The bakers at
    7·1 answer
  • The table shows the amounts y (in tons) of waste left in a landfill after x months of waste relocation. Use the table to complet
    12·1 answer
  • Seven is more than 2 plus a number,q, can be shown by the inequality 2+q<7. which causes for q make this a true statement.
    10·1 answer
  • Identify the equation in slope-intercept form for the line containing the point (2,1) and parallel to y=5/3x−1/3.
    6·1 answer
  • Find the missing side of the triangle shown below, if the perimeter is 81.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!