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Answer:
longer leg: 20 in
shorter leg: 15 in
hypotenuse: 25 in
Formulas:
Pythagorean Theorem
[tex]c^2 = a^2 + b^2[/tex]
c ... hypotenuse
a ... one leg
b ... another leg
Pythagorean theorem is used in right triangles (triangles in which one angle is 90°).
Step-by-step explanation:
longer leg: x
shorter leg: x - 5
hypotenuse: x + 5
To find x (longer leg), let's use Pythagorean theorem.
[tex]c^2 = a^2 + b^2\\(x+5)^2 = x^2 + (x-5)^2\\x^2 + 10x + 25= x^2 + x^2 -10x + 25\\x^2 + 10x = 2x^2 - 10x\\0 = x^2 - 20x[/tex]
Now let's factorize to get solutions for x.
[tex]0 = x(x-20)[/tex]
First solution:
[tex]x = 0[/tex]
Second solution:
[tex]x - 20 = 0\\x = 20[/tex]
Since a side of a triangle has to be a positive number, x is equal to 20.
Now let's just substitute x back to get side lengths. From the question the lengths are in inches.
longer leg: x = 20 in
shorter leg: x - 5 = 20 - 5 = 15 in
hypotenuse: x + 5 = 20 + 5 = 25 in