0
votes
1answer
127 views

Maximum area of a rectangle inside a triangle

I recently came across a problem where it gave a triangle with integer side lengths, and it asked you to find the maximum area of a rectangle of a triangle. I solved the problem correctly, but it ...
2
votes
0answers
55 views

Minimize the perimiter of a triangle with an inscribed circle

A circle touches the two legs of an angle. How can one draw a line that intersects both legs, such that the circle lies within the triangle with as sides the two legs and the drawn line, and such that ...
0
votes
2answers
570 views

What is the maximum area of a square inscribed in an equilateral triangle?

What is the maximum area of a square inscribed in an equilateral triangle? Please post the approach to solve the above question.
2
votes
2answers
108 views

When does the triangle have the smallest area?

The following triangle has an area $S$, and the sides $AO$ and $BO$ have the length $a$ and $b$, respectively. There is a fixed point $X$ at $(x,y)$. A point $C$ is put on the line segment $OA$, and ...
-1
votes
2answers
75 views

Two objects travel on a 2 dimensional grid. How can i find the angle that must be taken in order for the interception time to be the smallest [closed]

An object (a) travels on a linear path at constant speed. A second object (b) must intercept object a in the shortest amount of time possible. Object b is also at a set speed and can travel in any ...
1
vote
2answers
89 views

Minimizing area of a triangle with two fixed point and a point on parabola

A triangle is made up of three points, $A, B$, and $P$. $A(-1, 0)$ $B(0, 1)$ $P$ is a point on $y^2 = x$ Minimize the area of Triangle $ABP$. My approach is far too complicated, which ...
3
votes
4answers
195 views

Maximum surface inside a triangle

If I have a triangle with sides of length a, b, c and I have a rope of length L, what is the maximum surface of a boundary I can form with that rope that is entirely inside the triangle. Normally, ...
4
votes
2answers
115 views

Minimizing the length of a pipeline between cities

I have been trying to minimize piping going to two different cities. City A is located at $(0,4)$ and city B is located at $(6,3)$. The cities must connect to the $x$-axis (the main pipe line.) It ...