This creates a right triangle. One leg of the triangle is 25 feet and the other is 10 feet. To find the length of the ladder, we must use Pythagorean theorem.
a = 25
b = 10
c = ?
(25)^2 + (10)^2 = c^2. Square all the terms to the left of the equation and add them together.
725 = c^2. Take the square root of each side.
c = 26.93 feet.
The ladder needs to be 26.93 feet tall.
9x^2 -c =d
add c to each side
9x^2 = c+d
divide by 9
x^2=(c+d)/9
take the square root on each side
x = +- sqrt ((c+d)/9)
simplify
x = +- 1/3 sqrt (c+d)
Answer: 1/3 sqrt (c+d), - 1/3 sqrt (c+d)
The answer for this question would be 24 because 0 is included.
This is known as Einstein's proof, not because he was the first to come up with it, but because he came up with it as a 15 year old boy.
Here the problem is justification step 2. The written equation
BC ÷ DC = BC ÷ AC
is incorrect, and wouldn't get us our statement 2, which is correct.
For similar triangles we have to carefully pair the corresponding parts to get our ratios right:
ABC ~ BDC means AB:BD = BC:DC = AC:BC so BC/DC=AC/BC.
Justification 2 has the final division upside down.
