What is the perimeter of a computer graphic with sides measuring?
2√18, 2√32, 2√50, and 3√12 centimeters
The perimeter is _______ centimeters.
change all to something multiplied by sqrt2, then add
To find the perimeter of a shape, you simply need to add up the lengths of all its sides. In this case, we have a computer graphic with four sides, each given in terms of square roots.
The given side measurements are:
Side 1: 2√18 centimeters
Side 2: 2√32 centimeters
Side 3: 2√50 centimeters
Side 4: 3√12 centimeters
To find the perimeter, we will add all these side lengths together.
Perimeter = Side 1 + Side 2 + Side 3 + Side 4
Now, let's substitute the given side lengths into the formula:
Perimeter = 2√18 + 2√32 + 2√50 + 3√12
To simplify the square roots, we can factor out the largest perfect square possible from inside the radical symbols:
√18 = √(9 * 2) = 3√2
√32 = √(16 * 2) = 4√2
√50 = √(25 * 2) = 5√2
√12 = √(4 * 3) = 2√3
Now, we can substitute these simplified values back into the formula:
Perimeter = 2(3√2) + 2(4√2) + 2(5√2) + 3(2√3)
Simplifying further:
Perimeter = 6√2 + 8√2 + 10√2 + 6√3
Now, we can combine like terms by adding the coefficients of the square roots:
Perimeter = (6 + 8 + 10)√2 + 6√3
Perimeter = 24√2 + 6√3
Therefore, the perimeter of the computer graphic is 24√2 + 6√3 centimeters.