Consider an isosceles triangle of fixed perimeter P.

a) If x equals the length of one of the two equal sides, express the area A as a function of x.

b) What is the domain of A?

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- Jan 3rd 2010, 06:11 AMdartanian24Isosceles triangle of fixed perimeter P
Consider an isosceles triangle of fixed perimeter P.

a) If x equals the length of one of the two equal sides, express the area A as a function of x.

b) What is the domain of A? - Jan 3rd 2010, 07:07 AMabender
1)

(Note that A(x) above IS a function of x (and not x and P), since P is a fixed constant.)

2)

Enjoy your Sunday! - Jan 3rd 2010, 07:11 AMWilmer
- Jan 3rd 2010, 07:17 AMabender
- Jan 3rd 2010, 08:17 AMSoroban
Hello, dartanian24!

Quote:

Consider an isosceles triangle of fixed perimeter .

a) If equals the length of one of the two equal sides,

. . express the area as a function of

Code:`A`

*

/|\

/ | \

/ | \

x / | \ x

/ |h \

/ | \

/ | \

B *-------*-------* C

½b D ½b

: - - - b - - - :

Let = height of the triangle.

Then: .

In right triangle

Substitute [2]: .

Multiply by 4: .

Hence: .

We know that: .

Subnstitute [1] and [3]: .

Therefore: .

Quote:

b) What is the domain of ?

The area has a minimum of 0 . . . when

The area is a maximum when the triangle is.*equilateral*

. . Then: .

. . The area is: .

The range is: .