i need this answer

Question

Pennants are in the shape of an isosceles triangle (a triangle in which two sides are equal). See figure. Suppose the perimeter of a pennant is 30 inches. Find a function that models the area of the pennant, A, in terms of the length of one of the equal sides x. You do not have to simplify your answ

Answer 1

y is the base measure.

Perimeter P = 30 = 2x+y

y = 30 -2x

Dropping height h to the base produces 2 congruent right triangles

with hypotenuse x, and legs y/2 and h

Pythagorean says sqrt ( x^2 - (y/2)^2) = h

sqrt ( x^2 - (1/4)y^2) = h

sqrt( x^2 - (1/4) ( 30 -2x)^2) = h

sqrt( x^2 - (1/4) ( 900 - 120x + 4x^2) = h

sqrt( x^2 - 225 + 30x - x^2) = h

sqrt( 30x - 225) = h

The area is (1/2) y h =

(1/2) ( 30 -2x) sqrt(30x - 225) = A(x)