One leg of a right triangle has a length of 55 m. the other sides have lengths that are consecutive integers. find these lengths.

First let us assign the variables for the two lengths:

x = 1st integer

x + 1 = 2nd consecutive integer = the hypotenuse of the right triangle

The 2nd consecutive integer should be the hypotenuse since its value should be highest among the three sides.

Now using the hypotenuse formula we calculate for x:

(x + 1)^2 = 5^2 + x^2

x^2 + 2x + 1 = 25 + x^2

2x + 1 = 25

2x = 24

x = 12 m

So other integer is

 x + 1 = 13 m

Therefore the other sides are 12 m and 13 m.

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°

a

step-by-step explanation: