Find the area of the largest rectangle that can be inscribed in a right triangle with legs of lengths 4 cm and 6 cm if two sides of the rectangle lie along the legs. webassign cengage

Step-by-step explanation:

Let x and y be the sides of the rectangle.

Area of the Triangle, A(x,y)=xy

From the diagram, Triangle ABC is similar to Triangle AKL

AK=4-y

Therefore:

We substitute x into A(x,y)

We are required to find the maximum area. This is done by finding

the derivative of Aand solving for the critical points.

Derivative of A:

Recall that: x=6-1.5y

x=6-1.5(2)

x=6-3

x=3cm

Therefore, the maximum rectangle area is:

Area =3 X 2 =

answer: 457.14

step-by-step explanation:

205 - 45 = 160

160 / .35 = 457.142857