The shorter leg of a right triangle is 14 feet less than the other leg. Find the length of the two legs of the hypotenuse is 25 feet.

  9.233 ft, 23.233 ft

Step-by-step explanation:

If the shorter leg is x, then the longer leg is x+14 and the Pythagorean theorem tells you ...

  x^2 + (x +14)^2 = 25^2

  2x^2 +28x +196 = 625

  x^2 +14x = 214.5

  x^2 +14x +49 = 263.5

  (x +7)^2 = 263.5

  x = -7 +√263.5 ≈ 9.23268

The two leg lengths are √263.5 ± 7 feet, {9.23 ft, 23.23 ft}.

9 ft, 23 ft

Step-by-step explanation:

We know the Pythagorean Theorem is a²+b²=c². Since one leg is 14 less than the other leg, we can use x-14 and the other leg would be x. We can plug these into the Pythagorean Theorem with the given hypotenuse.

(x-14)²+x²=25²

(x²-28x+196)+x²=625

2x²-28x+196=625

2x²-28x-429=0

When we solve for x, we get and .

Note, since we rounded to 23, the hypotenuse isn't exactly 25, but it gets very close.

since proposition states that a number is greater than 25, if is true then the number must actually be greater than 25.

this implies that all possible options, except 24, can be accepted

the answer is (4,3)

since the rule for r0, 90º is (-y,x) and it was already applied to form the image, all you have to do is reverse the answer using this formula.