# Optimization questions to get ready for a test

• NogardMX
In summary, the question asks for the area of a isosceles triangle with the largest possible area that can be inscribed in a circle of given radius. The answer is found by using the equation for the area of a triangle, which depends on the lengths of the sides and the angle between them.

#### NogardMX

I was doing some optimization questions to get ready for a test. I came across one that stumped me. The question was "Find the dimensions of the isosceles triangle of the largest area that can be inscribed in a circle of radius r".

My approach was:
let y be the base of triangle
let x be the two equal sides of triange.

A(t) = (bh)/2
= (y*(x^2-(y/2)^2)^1/2))/2

I can't find the equation to relate the radius to the area. help?

Let the angle between the two longer sides be t, now imagine instead of drawing lines from the short edge's ends to the perimeter, you drew the lines to the centre of the circle, the angle these shorter sides (of length r) create would be 2t. There is a formula for finding the area in terms of sides and angles between sides, and t depends on the lengths chosen originally. This might help you.

matt grime said:
Let the angle between the two longer sides be t, now imagine instead of drawing lines from the short edge's ends to the perimeter, you drew the lines to the centre of the circle, the angle these shorter sides (of length r) create would be 2t. There is a formula for finding the area in terms of sides and angles between sides, and t depends on the lengths chosen originally. This might help you.

What do you mean by "now imagine instead of drawing lines from the short edge's ends to the perimeter, you drew the lines to the centre of the circle, the angle these shorter sides (of length r) create would be 2t. "?

the formula for the area in terms of the sides of a triangle is

(s(s-a)(s-b)(s-c))^1/2

where s is (a+b+c)/2
and a,b,c are the side lengths.

is that it?

## 1. What is optimization?

Optimization is the process of finding the best solution to a problem within a given set of constraints. It involves maximizing or minimizing a certain objective function while adhering to any limitations or restrictions.

## 2. How is optimization related to test preparation?

Optimization can be applied to test preparation by identifying the most efficient and effective methods for studying and retaining information. It can also be used to prioritize and allocate study time and resources to areas that need the most improvement.

## 3. What are some common optimization techniques for test preparation?

Some common optimization techniques for test preparation include creating a study schedule, organizing study materials, using mnemonic devices, practicing past exams, and seeking help from teachers or tutors.

## 4. How can optimization help improve test scores?

Optimization can help improve test scores by streamlining the studying process and focusing on areas that need the most attention. It can also help reduce test anxiety by providing a structured and efficient approach to test preparation.

## 5. Are there any limitations to using optimization for test preparation?

While optimization can be a useful tool for test preparation, it is important to keep in mind that every individual learns and retains information differently. What works for one person may not work for another, so it is important to adapt and personalize study methods accordingly.