ASAP WITH THIS MATH HELP

Problem 2 9 cm and 12 cm.

Explanation:

c^2 = a^2 + b^2

c^2 = 15^2

c^2 = 225

a = b+3

a^2 + b^2 = 225

(b+3)^2 + b^2 = 225

(b+3)(b+3) + b^2 = 225

Use FOIL on the first term.

b^2 +3b +3b + 9 +b^2 = 225

Collect terms.

2b^2 +6b + 9 = 225

Subtract 225 from both sides

2b^2 +6b -216 = 0

Divide both sides by 2 to eliminate the coefficient on b^2.

b^2 +3b -108 = 0

Factor

(b+12)(b-9) = 0

So, b=-12 or b=9.

A negative length does not make sense, so b=9.

Use the Pythagorean to find side a.

a^2 = c^2 - b^2

a^2 = 225 - 81

a^2 = 144

a = 12

So, the lengths of the two legs are 9 cm and 12 cm.

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