Math Help: Solve 2 Questions with Isoceles Triangle

[ohlhauc1]

I have two questions that I need help with. I desperately need help with them. They are:

1. The coordinates of points P and Q are (1,2) and (2,-3) respectively, and R is a point on the line x=-1. Find the coordinates of R so that PR + RQ is a minimum.



2. An isoceles triangle has a base of 6m and a height of 4m with a rectangle in it that touches all three sides so that there is a rectangle, triangle on top, and two triangles on the sides. (Sorry for the description, but I couldn't put the image here).

a) Find the maximum area and dimensions of the rectangle within the triangle.
b) Repeat part a) for a rectangle inside a isoceles triangle with a base of 4m and a height of 12m.
c) Compare the dimensions of the base and height of each isosceles triagnle with the dimensions of each rectangle found in parts a) and b). What do you notice?

 

[xman]

first, question is
$$PR + RQ$$
the corresponding distances between the points?
second question, i am not picturing your description of the geometry, what do you mean there is an isoceles triangle with a rectangle in it?

 

[HallsofIvy]

ohlhauc1, Please show what you have already done on this problem.

 

[VietDao29]

I have two questions that I need help with. I desperately need help with them. They are:

1. The coordinates of points P and Q are (1,2) and (2,-3) respectively, and R is a point on the line x=-1. Find the coordinates of R so that PR + RQ is a minimum.



2. An isoceles triangle has a base of 6m and a height of 4m with a rectangle in it that touches all three sides so that there is a rectangle, triangle on top, and two triangles on the sides. (Sorry for the description, but I couldn't put the image here).

a) Find the maximum area and dimensions of the rectangle within the triangle.
b) Repeat part a) for a rectangle inside a isoceles triangle with a base of 4m and a height of 12m.
c) Compare the dimensions of the base and height of each isosceles triagnle with the dimensions of each rectangle found in parts a) and b). What do you notice?

I'll give you some hints to start off the problem, in case you don't know where to start:
For 1. You should use triangle inequality.
For 2. The first thing you have to do is to find the relation between the width, and the length of the rectangle.
Can you go from here? :)