There are points on a grid at (0,0) and (3,0). a. What is a possible coordinate of the third vertex if the triangle has a perimeter of 11 units? Explain.
b. Is there another point that could be the third vertex? Explain.
a. Suppose the triangle is an isosceles triangle in quadrant I with base 3 units. Then, each of the other
sides would measure units. This isosceles triangle is made up of two triangles each with a base of
units and a hypotenuse of units. The height of the right triangle is approximately units. So,
the coordinates of the third vertex are.
(Type an ordered pair, using integers or decimals. Round to the nearest tenth as needed.)

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

5 + 8 +7 + 4 + 0 +1 = 25

step-by-step explanation:

x^3-4x^2+3x-2/x^2+1

step-by-step explanation:

factor the numerator and denominator and cancel the common factors