Question

jaos work
line 1: ( 9 ^ { 2 } + x ^ { 2 } = 12 ^ { 2 } )
line 2: ( 81 + x ^ { 2 } = 144 )
line 3: ( - 81 - 81 )
line 4: ( sqrt { x ^ { 2 } } = sqrt { 63 } )( x = 9 sqrt { 7 } )
a right triangle has a hypotenuse of 12 units and a leg of 9 units. jaos work for finding the missing leg of the right triangle is shown. is he correct? if not, identify his mistake.
jao is incorrect. in line 1, he should have used the equation ( 9 ^ { 2 } + 12 ^ { 2 } = x ^ { 2 } ).
jao is correct.
jao is incorrect. he made a mistake in line 3 because ( 144 - 81 ) is not 63.
jao is incorrect. in line 4, the correctly simplified square root is ( 3 sqrt { 7 } )

Explanation:

Step1: Recall Pythagorean theorem

For right triangle: $a^2 + b^2 = c^2$ (c=hypotenuse, a,b=legs). Jao mixed up hypotenuse and leg: should be $9^2 + x^2 = 12^2$ instead of $9^2 + x^2 = 12^2$ (wait, no—wait Jao wrote Line1: $9^2 + x^2 =12^2$ which is correct? Wait no, wait the problem says hypotenuse is 12, so yes: leg² + leg² = hypotenuse². Then Line2: 81 + x²=144 (correct). Line3: x²=144-81=63 (correct), so $\sqrt{x²}=\sqrt{63}$ (correct). Line4: $\sqrt{63}=3\sqrt{7}$, not $9\sqrt{7}$. So Jao's mistake is in Line4.

Answer:

Jao is incorrect. In Line 4, the correct simplified square root is $3\sqrt{7}$ (assuming the last option is this, as per the image's last choice description).

(Note: Based on the multiple-choice options provided, the correct answer is the last option: "Jao is incorrect. In Line 4, the correctly simplified square root is $3\sqrt{7}$".)