Question

H

請問這題怎麼算

9. A rectangle is inscribed in a right triangle, as 000,00
shown in the accompanying figure. If the triangle 0
has sides of length 5, 12, and 13, what are the

dimensions of the inscribed rectangle of greatest
area?
365
olle i gnitu9
baigs Cost
ieu
13
12
5
2000 time

微積分

Answer 1

✨ 最佳解答 ✨

Alstormeria5

Simple way

Answer 2

綾

令0 < 5x < 5 => 0 < x < 1
（設5x是方便計算）
5x*5(1-x)=-25x^2+25x=-25(x^2-x+1/4)+25/4=-25(x-1/2)^2+25/4
根據二次函數的圖形可知
當x = 1/2 時
長方形面積有最大值25/4