Question

Which is the length of the hypotenuse for a right triangle with leg a = 8 and leg b = 15 cm?

Answer 1

Answer:

$\huge{ \boxed{ \tt{17 \: cm}}}$

Option D is the correct choice.

☪ First , Let's know about right triangle , legs and hypotenuse :

• A right triangle is a triangle with an angle of 90°.
• The two sides that form the right angle are called legs.
• The opposite side of right angle is the hypotenuse.

☥ Let's explore about The Pythagorean Theorem :

• Pythagoras was one of the first mathematician to recognize the relationship between the sides of a right triangle. This special relationship forms ' The Pythagorean Theorem '.
• The Pythagorean theorem states that the sum of the squares of the legs of a right triangle equals the square of the length of a hypotenuse.
• In algebraic terms , The Pythagorean Theorem is stated as : $\boxed{ \sf{ {a}^{2} + {b}^{2} = {c}^{2} }}$

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☯ Now , let's start to solve :

✑ $\underline{ \underline{ \text{Given}}} :$

• a = 8 cm , b = 15 cm

✑ $\underline{ \underline{ \text{To\: Find}}} :$

• Length of a hypotenuse ( c )

✐ $\underline{ \bold{ \underline{Using \: Pythagorean \: Theorem}}} \: :$

☞ $\boxed{ \bold{ \sf{ {a}^{2} + {b}^{2} = {c}^{2} }}}$

Substitute the known values :

↦ $\sf{ {8}^{2} + {15}^{2} = {c}^{2}}$

↦ $\sf{64 + 225 = {c}^{2} }$

↦ $\sf{289 = {c}^{2} }$

↦ $\sf{ {c}^{2} = 289 }$

Take the square roots of both sides :

↦ $\sf{ \sqrt{ {c}^{2} } = \sqrt{289}}$

↦ $\boxed{ \sf{c = 17 \: cm}}$

The length of the hypotenuse is $\boxed{ \bold{ \text{17 \: cm}}}$.

And we're done!!

Hope I helped!

Have a wonderful day ! ツ

~TheAnimeGirl ♡

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