Thread: Calculus Optimizing Problem--Held Needed

Hi, I need some help on how to do the following question.

Find the area of the largest rectangle that can be inscribed in a right triangle with legs adjacent to the right angle of lengths 5cm and 12 cm. The two sides of the rectangle lie along the legs

Final Answer: 15cm squared

Use similar triangles.

A=xy

But by similar triangles, x/5=(12-y)/12

So, y=12-(12x/5)

A=x(12-(12x/5))

dA/dx=12-(24x/5)

12-(24x/5)=0

x=5/2 and y=6

A=xy=(5/2)(6)=15