1. ## optimzation problem #6

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

2. Originally Posted by skeske1234
Find the area of the largest rectangle that can be inscribed in a right triangle with legs adjacent to the right angle of the lengths 5 cm and 12 cm. The two sides of the rectangle lie along the legs.
sketch the right triangle with vertices (0,0) , (0,5) , and (12,0)

one corner of the rectangle lies on the line between (0,5) , and (12,0).

you need to find the equation of this line.

area of the rectangle will be A = xy , where y is the linear equation mentioned above.

find $\displaystyle \frac{dA}{dx}$ and maximize.

3. Originally Posted by skeeter
sketch the right triangle with vertices (0,0) , (0,5) , and (12,0)

one corner of the rectangle lies on the line between (0,5) , and (12,0).

you need to find the equation of this line.

area of the rectangle will be A = xy , where y is the linear equation mentioned above.

find $\displaystyle \frac{dA}{dx}$ and maximize.
Hi can you double check my equation before i proceed?

i have

x^2+y^2=r^2
12^+5^2=169^2
x^2+y^2=169^2
y=(169^2-x^2)^0.5

4. Originally Posted by skeske1234
Hi can you double check my equation before i proceed?

i have

x^2+y^2=r^2
12^+5^2=169^2
x^2+y^2=169^2
y=(169^2-x^2)^0.5
sorry, no Pythagoras for this problem ...

do you understand that you're maximizing the area of a rectangle inscribed in a triangle?

5. Originally Posted by skeeter
sorry, no Pythagoras for this problem ...

do you understand that you're maximizing the area of a rectangle inscribed in a triangle?
oh.. yes.. but I am having trouble coming up with the linear equation.

6. Originally Posted by skeske1234
oh.. yes.. but I am having trouble coming up with the linear equation.
here's a picture. y = mx+b, remember?