the rectangle with a side of length 12cm has a diagonal of 15cm. what is the perimeter of the rectangle?

42 cm

Step-by-step explanation:

First since the second side length is unknow we need to find it.

We will use the Pythagorean theorem which is

Since we will be solving for b we will rearrange the equation to be

now to slove input the data we know

= 144 - 225

= 81

= 9

With the two sides we simply add up all the sides for the perimeter

9+12+9+12 = 42

the answer is 13 cm

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.