The hypotenuse of a right triangle is 13 inches. Its perimeter is 30 inches. Find the length of its hypotenuse.

Wording is in mistake: Hypotenuse is given 13 inches

It must be asking to find the lengths of the legs of the triangle

legs ( a, b)

Hypotenuse ---c

a^2 + b^2 = c^2 / Pythagoras theorem

a + b + c = P / Perimeter of the triangle

a^2 + b^2 = 13^2 = 169

a + b = 30 -c = 17

From 2nd equation:

b = 17 -a

Substitute back into 1st equation:

a^2 + ( 17 - a ) ^2 = 169

a^2 + a^2 -34a + 289 = 169

2a^2 - 34a + 120 =0

a^2 - 17a +60 =0

(a - 12) ( a- 5 ) =0

a = 12 a = 5

a = 12, b = 5 / lengths of the legs of the triangle.

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