The sides have to change - the Pythagorean Theorem most definitely applies to this problem. The only thing that is constant is the hypotenuse.justindizzle said:on second thought i don't think the pythagorean theorem would be relevant to the equation because the sides of the triangle are not changing and the derivative would imply that they do
?justindizzle said:i think you can actually use both formulas
rearrange the pythagorean formula so that : b=10-a
justindizzle said:(hypotenuse was 10) so a^2 + b^2 = 10^2
then substitute it into the base height formula :
= a(10-a) / 2
=10a - a^2 / 2
however when i solved for A and B i got 5*5/2 which = 12.5 but the answer is 25. what am i doing wrong ?
No. What you're saying is that, for example, [itex]\sqrt{5^2 - 3^2} = 5 - 3 = 2[/itex], which is not true.justindizzle said:okay so we know the triangle is a right triangle, and that the hypotenuse has a length of 10cm. We're trying to find the max area.
Pythagorean formula
a^2 + b^2 = c^2 (C = hypotenuse)
so according to what were given a^2 + b^2 = 10^
a^2 + b^2 = 100
we can rearrange this much into
b^2 = 100-a^2
and if you square root the whole equation it simplifies too
b=10-a correct?
justindizzle said:i then substituted that into the base height formula which is (1/2)ab
=(1/2)a(10-a)
=(1/2)(10a-a^2)
=(5a)-(1/2)a^2 <--- multiplied the (1/2) in
=then i took the derivative to solve for A
=5-a
= a=5
Then putting "A" back into out previous formula b=10-a to solve for "b"
b=5
according to the b*h formula the area would be 5*5/2 = 12.5
but the answer is 25 in the back of the book ?
You have b2 = 100 - a2. Then b = ±[itex]\sqrt{100 - a^2}[/itex]. Your mistake earlier was in thinking you could simplify this further.justindizzle said:i'm hooped
how do i solve for b then ?
This is not an equation. An equation has an = in it somewhere.justindizzle said:or can i square the entire equation into
a2*b2*(1/4)
justindizzle said:Homework Statement
The hypotenuse of a right triangle has length of 10cm. Determine its maximum possible area.
c= 10cm
Homework Equations
a^2 + b^2 = c^2 ?
b*h*(1/2)
The Attempt at a Solution
just drew out the triangle so far, confused as to where to go from here
i assume ill be taking the derivative of some equation to find the max
justindizzle said:i'm hooped
how do i solve for b then ?
or can i square the entire equation into
a2*b2*(1/4)
The formula for finding the maximum area of a triangle is A = 1/2 * b * h, where b is the base of the triangle and h is the height. This formula is derived from the fact that the area of a triangle is equal to half the product of its base and height.
The base and height of a triangle can be determined by measuring the two sides that form a right angle, or by using the Pythagorean theorem to find the missing side. The side opposite the right angle is considered the height, and the other side is considered the base.
No, the maximum area of a triangle can only be found using the base and height. In order to use the formula A = 1/2 * b * h, the base and height must be known. If only three sides are given, it may be possible to find the base and height using trigonometric functions, but it is not guaranteed.
No, the maximum area of a triangle is not affected by the shape of the triangle. As long as the base and height are known, the formula A = 1/2 * b * h can be used to find the maximum area, regardless of the shape of the triangle.
You can check the accuracy of your calculated maximum area by using a different method to find the area, such as using Heron's formula or breaking the triangle into smaller right triangles and adding their areas together. If you get the same result, then your calculated maximum area is likely correct.