Find the area of the largest rectangle that can be inscribed in a right triangle with legs of lengths 3 cm and 8 cm if two sides of the rectangle lie along the legs.

Question

dumbcow · Answer

|dw:1383721137963:dw|
find x,y which maximize area
first get "y" in terms of "x" using proportions
$$\frac{y}{3-x} = \frac{8}{3}$$
$$y = 8-\frac{8}{3}x$$
define Area function
$$A = x*y = x(8-\frac{8}{3}x)$$
take derivative and set equal to 0
$$A' = 8-\frac{16}{3}x = 0$$
$$x = \frac{3}{2}$$
thus
$$y = 4$$

mony01 · Answer

so is 4 the area?

dumbcow · Answer

wow you didnt follow anything i did huh

mony01 · Answer

to get the area dont you multiply x and y

dumbcow · Answer

yes correct :)

mony01 · Answer

so the area is 6

dumbcow · Answer

yep

mony01 · Answer

thank you so much oh and sorry for the first reply...Dont know what I was thinking..

dumbcow · Answer

yw and its ok, sometimes i get too many stupid replies from other users so it lessens my patience

dumbcow · Answer

too many times they just look at the last line and assume that must be the answer :{