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KiRa [710]
3 years ago
7

The hypotenuse of a 45°-45°-90° triangle measures 18 cm. A right triangle is shown. The other 2 angle measures are 45 degrees. T

he length of the hypotenuse is 18 centimeters. What is the length of one leg of the triangle? 9 cm 9 StartRoot 2 EndRoot cm 18 cm
Mathematics
1 answer:
Novosadov [1.4K]3 years ago
8 0

Answer:

9 \sqrt{2}\ cm

Step-by-step explanation:

Given

Hypotenus = 18cm

Required

Find the length of the other two sides

From the question, we understand that the other two sides are equal; let's represent them with x.

Pythagoras theorrem states that:

Hypotenuse^2 = x^2 + x^2

Substitute 18 for Hypotenuse

18^2 = x^2 + x^2

18^2 = 2x^2

18 * 18 = 2x^2

324 = 2x^2

Divide both sides by 2

\frac{324}{2} = \frac{2x^2}{2}

162 = x^2

Take root of both sides

\sqrt{162}  = \sqrt{x^2}

\sqrt{162}  = x

x = \sqrt{162}

x = \sqrt{81 * 2}

Split the above

x = \sqrt{81} *\sqrt{2}

x = 9 *\sqrt{2}

x = 9 \sqrt{2}

Hence, the length of one leg is 9 \sqrt{2}\ cm

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