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Math  /  Geometry

Question15.

Studdy Solution

STEP 1

1. The triangle is a right triangle.
2. We can use the Pythagorean theorem to find the length of the missing leg.
3. The Pythagorean theorem states: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs.

STEP 2

1. Express the Pythagorean theorem for the given triangle.
2. Substitute the given values into the Pythagorean theorem.
3. Solve for the unknown leg xx.
4. Verify that the solution satisfies the original equation.

STEP 3

Express the Pythagorean theorem for the given triangle. (35)2+x2=(52)2 (3\sqrt{5})^2 + x^2 = (5\sqrt{2})^2

STEP 4

Substitute the given values into the Pythagorean theorem and simplify. (35)2+x2=(52)2 (3\sqrt{5})^2 + x^2 = (5\sqrt{2})^2 (32)(52)+x2=(52)(22) (3^2)(\sqrt{5}^2) + x^2 = (5^2)(\sqrt{2}^2) 9⋅5+x2=25⋅2 9 \cdot 5 + x^2 = 25 \cdot 2 45+x2=50 45 + x^2 = 50

STEP 5

Solve for the unknown leg xx. x2=50−45 x^2 = 50 - 45 x2=5 x^2 = 5 x=5 x = \sqrt{5}

STEP 6

Verify that the solution satisfies the original equation. (35)2+(5)2=(52)2 (3\sqrt{5})^2 + (\sqrt{5})^2 = (5\sqrt{2})^2 45+5=50 45 + 5 = 50 50=50 50 = 50 The solution satisfies the original equation.
The length of the other leg xx is: x=5 x = \sqrt{5}

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