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Answer:

Final answer is E. 10

Step-by-step explanation:

Apply Pythagorean theorem to the given right triangle.

[tex]\left(Hypotenuse\right)^2=\left(Leg_1\right)^2+\left(Leg_2\right)^2[/tex]

[tex]\left(h\right)^2=\left(5\sqrt{2}\right)^2+\left(5\sqrt{2}\right)^2[/tex]

[tex]\left(h\right)^2=50+50[/tex]

[tex]\left(h\right)^2=100[/tex]

take square root of both sides

[tex]h=10[/tex]

Hence final answer is E. 10

kudzordzifrancis

ANSWER

E. 10

EXPLANATION

Using Pythagoras Theorem, which says the hypotenuse squared is equal to the sum of squares of the two shorter legs.

[tex] {h}^{2} = {(5 \sqrt{2} )}^{2} + {(5 \sqrt{2} )}^{2} [/tex]

Evaluate the squares on the RHS.

[tex] {h}^{2} = 25 \times 2 + 25 \times 2[/tex]

[tex] {h}^{2} = 50 + 50[/tex]

Simplify:

[tex] {h}^{2} = 100[/tex]

Take positive square root.

[tex]h = \sqrt{100} [/tex]

[tex]h = 10[/tex]

The hypotenuse is 10 units.

The correct answer is E

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