The shortest side of a triangle measures 15 inches less than the longest side. If the third side is 2 inches shorter than the longest side and the perimeter is 103 inches, find the measure of the 3 sides.

Step-by-step explanation:

Let x represent the length of the longest side of the triangle.

The shortest side of a triangle measures 15 inches less than the longest side. It means that the length of the shortest side is x - 15.

If the third side is 2 inches shorter than the longest side, it means that the length of the third side is

x - 2

The formula for determining the perimeter of a triangle is

Perimeter = a + b + c

Where a, b and c are the lengths of each side of the triangle. The perimeter of the triangle is 103 inches. It means that

x + x - 15 + x - 2 = 103

3x - 17 = 103

3x = 103 + 17 = 120

x = 120/3

x = 40

The length of the longest side is

40 inches

The length of the third side is

40 - 2 = 38 inches

The length of the shortest side is

40 - 15 = 25 inches

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.