Question

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?​

Answer 1

11 m and 14 m

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