The right side of a right triangle is divided into 40 cm and 10 cm. Cut out a square and make it as large as possible. What is the square area Sorry, wrong number. Change the word "person" to "person", Can you solve it arithmetically?

The maximum area of a square is 64 square centimeters
Let the side length of a square be a
Then (40-A) / a = A / (10-A)
The solution is: a = 8
So the square area s = 8 * 8 = 64

A right triangle, the two right sides are 10 cm and 30 cm respectively. If you cut a square as large as possible in it, how large is the square
For a right triangle, the two right sides are 10 cm and 30 cm respectively. If you cut a square as large as possible inside, what is the area of the square?

The right sides of a right triangle should be the two sides of the square with the largest area,
Let the side length of a square be a,
Then the small square divides the original triangle into three parts
1/2a(10-a)+1/2a*(30-a)+a*a=1/2*10*30
a=7.5
So area: a * a = 56.25

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