Figure ABCDE is a regular pentagon. Segment AE is located at A (2, 1) and E (4, 1). What is the perimeter of ABCDE?

4 units
6 units
8 units
10 units

Correct option: fourth one -> 10 units

Step-by-step explanation:

As the pentagon is regular, all the sides have the same length, so we just need to find the length of the side AE and then multiply by 5.

To find the length of AE we can find the distance from point A to point E:

distance from A to E:

sqrt( (4-2)^2 + (1-1)^2) = 2 units

To the perimeter of the pentagon is 5 * 2 = 10 units.

Correct option: fourth one

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

828. all there is to it!

here, if you ever need with rounding (or other forms of arithmetic/math) again, use this:

thats the rounding one, but if you just click the top left, it shows you all the calculators you may need!