A window is to be built in the shape of a rectangle surmounted by an isosceles triangle. The area of the window must be 6 square meters. Use Lagrange Multipliers to find the width and height of the rectangle for which the perimeter of the window will be as small as possible

x = 2.536 m

y = 2 m

Step-by-step explanation:

Considering the three sides of the rectangle and the isosceles triangle

when resolving the width and height of the rectangle to achieve the smallest possible perimeter.

step 1 :

Area of window =  xy + 1/2 xz  , perimeter = x + 2y + 2c

c =

we are tasked with minimizing the perimeter ( p ) subject to A = 6

attached below is the detailed solution of the given problem

answer: a and c are correct

step-by-step explanation:

the +5 is the vertical translation

the added negative symbol in front is the reflection over the y-axis