Find the lenght of the hypontenuse of a right triangle with legs of 9 cm and 12 cm. (a) 8 cm (b) 21 cm (c) 15 cm (d) 225 cm

The length of the hypotenuse is C. 15.

Step-by-step explanation:

Use the Pythagorean theorem. a^2 + b^2 = c^2

9^2 = 81

12^2 = 144

81 + 144 = 225

The square root of 225 is 15; 15^2.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°