the area of a right triangle is 77 m^2. the hypotenuse has a length of √317 m. what is the length of the legs?

11 m and 14 m

Step-by-step explanation:

Legs: x and y

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1/2xy = 77 ⇒ xy = 154

√x²+y² = √317 ⇒ x²+y²=317

x²+y²+2xy = (x+y) ² = 2*154+317 = 625 ⇒ x+y = √625 = 25

x = 25-y

xy=154 ⇒ y (25-y) = 154 ⇒ 25y - y²=154 ⇒ y² - 25y + 154=0 ⇒ y=11 and y=14

x = 25-y = 14 and 11