# calculus

Find the lenght of the sides of an isosceles triangle with a given perimeter if its area is to be as great as possible.

let k be the the length of the two iso sides, so the other side is P-2k. Call that the base.

Using Heron's formula:
Area=SQRT(s(s-a)(s-b)(s-c)),

but s= P/2 , a and b are equal, and c is P-2a

area= sqrt(s(s-a)^2 (s-P+2a))

dA/d=0= you do it. Solve for a

1. 👍 0
2. 👎 0
3. 👁 121

## Similar Questions

1. ### algebra

This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation 2a + b = 15.7 can be used to find the side lengths. If one

asked by Kris on October 13, 2014
2. ### math

In an isosceles triangle, the perimeter is 75 cm and one of the sides is 25 cm. Find all its sides. Can you find all angles of the triangle? Explain your answer.

asked by maria on January 28, 2017
3. ### geometry

The perimeter of an isosceles triangle is 42 cm . its base is 2/3 times the sum of the equal sides . find the length of each side and the area of the triangle.

asked by saurav kumar on December 30, 2010
4. ### Math

Can someone please check to see if I answered these true and false statements correctly? Thank you! 1. A triangle can have two right angles. (TRUE??) 2. An equilateral triangle is also an acute. (TRUE??) 3. A right triangle can

asked by Anonymous on November 9, 2014
5. ### High School Geometry

In isosceles ΔABC, AC = BC, AB = 6 in, CD ⊥ AB , and CD =√ 3 in. Find the perimeter of the isosceles triangle. Can u plz put answer and equation thanks, :)

asked by Alexa on February 25, 2017
1. ### math

3. An isosceles triangle has sides length xcm xcm and 9cm. B its perimeter is less than 24 and x is a whole number. I find the lowest value of x. II find the highest value of x

asked by LIVINUS CHIDERA on April 22, 2017
2. ### Algebra

An isosceles triangle has at least two congruent sides.the perimeter of a certain isosceles triangle is at most 12in. The length of each of the two congruent sides is 5in . What are possible lengths of the remaining side? A.s

asked by Need help on October 26, 2017
3. ### math

The base of an isosceles triangle is 4/3 cm.the perimeter of the triangle is 4 2/15cm. What is the length of either of the remaining equal sides

asked by Gousia on December 16, 2011
4. ### math

an isosceles triangle has a perimeter of (9y-15)cm.what is the length of each of the two equal sides,if its third sides is (3y-7)cm

asked by Cobbina on December 4, 2018
5. ### math

an isosceles triangle has perimeter of 15m. Find all integral possibilities for the lengths of the side in meters. Hint: the sum of the lengths of any two sides of a triangle must exceed the third side.

asked by emily on October 17, 2018
6. ### Maths

The perimeter of an isosceles triangle is 28cm. AB =4ycm,AC=(6y-2x+1)cm and BC =(x+2y)cm. Find x and y, state the lengths of the triangle.

asked by Temitope on January 8, 2018