What is the perimeter of a computer graphic with sides measuring:
2 times the square root of 50, 3 times the square of 72, 6 times the square root of 98, and 3 times the square root of 12 centimeters?
just add up the sides:
2√50 + 3√72 + 6√98 + 3√12
factor out perfect squares:
2*5√2 + 3*6√2 + 6*7√2 + 3*2√3
70√2 + 6√3
Ah, the perimeter of a computer graphic, you say? Well, let's crunch some numbers while keeping our sense of humor intact!
To find the perimeter, we simply add up all the sides:
2√50 + 3(√72)^2 + 6√98 + 3√12
Now, let me grab my calculator and get ready to clown around!
First, let's simplify the square roots:
2√50 = 2(5√2) = 10√2
√72 = √(36 x 2) = 6√2
√98 = √(49 x 2) = 7√2
√12 = √(4 x 3) = 2√3
Now, let's calculate:
10√2 + 3(6√2)^2 + 6(7√2) + 3(2√3)
Wait, wait, hold on a second! I can't resist adding a pinch of humor to this calculation.
Pardon the interruption, but have you ever seen a computer graphic going for a swim? It's just pixels diving into the deep end of the monitor!
Now, where were we? Ah, yes, back to calculating:
10√2 + 3(6√2)^2 + 6(7√2) + 3(2√3)
Using PEMDAS, we simplify the powers:
10√2 + 3(36 x 2) + 6(7√2) + 3(2√3)
Multiply the numbers:
10√2 + 3(72) + 6(7√2) + 3(2√3)
More calculations:
10√2 + 216 + 42√2 + 6√3
Phew, we're almost there! Time for more math:
Combine like terms:
(10√2 + 42√2) + (216 + 6√3)
That equals:
52√2 + (216 + 6√3)
Finally, let's add up everything:
52√2 + 216 + 6√3
And there you have it! The perimeter of that computer graphic measures approximately 52√2 + 216 + 6√3 centimeters, assuming my calculations didn't get lost in a virtual circus along the way!
To find the perimeter of a shape, you need to add up the lengths of all the sides.
Let's calculate the lengths of each side:
1. Side 1: 2 times the square root of 50 cm
Mathematically, side 1 = 2 * sqrt(50) cm = 2 * 7.07 cm = 14.14 cm
2. Side 2: 3 times the square of 72 cm
Mathematically, side 2 = 3 * (72)^2 cm = 3 * 5184 cm = 15,552 cm
3. Side 3: 6 times the square root of 98 cm
Mathematically, side 3 = 6 * sqrt(98) cm = 6 * 9.9 cm = 59.4 cm
4. Side 4: 3 times the square root of 12 cm
Mathematically, side 4 = 3 * sqrt(12) cm = 3 * 3.46 cm = 10.38 cm
Now, let's calculate the perimeter by adding all the sides:
Perimeter = side 1 + side 2 + side 3 + side 4
= 14.14 cm + 15,552 cm + 59.4 cm + 10.38 cm
= 15,635.92 cm
Therefore, the perimeter of the computer graphic is approximately 15,635.92 centimeters.
To find the perimeter of a computer graphic, you need to add up the lengths of all its sides.
In this case, the lengths of the sides are given as:
- 2 times the square root of 50 cm
- 3 times the square of 72 cm
- 6 times the square root of 98 cm
- 3 times the square root of 12 cm
To find the values of the square roots and squares, you can use a calculator. Let's break down the calculation step by step:
1. Calculate the square root of 50:
square root of 50 ≈ 7.071
2. Multiply the square root of 50 by 2:
2 * (square root of 50) ≈ 2 * 7.071 ≈ 14.142
3. Calculate the square of 72:
square of 72 = 72 * 72 = 5184
4. Multiply the square of 72 by 3:
3 * (square of 72) = 3 * 5184 = 15552
5. Calculate the square root of 98:
square root of 98 ≈ 9.899
6. Multiply the square root of 98 by 6:
6 * (square root of 98) ≈ 6 * 9.899 ≈ 59.394
7. Calculate the square root of 12:
square root of 12 ≈ 3.464
8. Multiply the square root of 12 by 3:
3 * (square root of 12) ≈ 3 * 3.464 ≈ 10.392
Now, add up all the side lengths to find the perimeter:
14.142 + 15552 + 59.394 + 10.392 ≈ 15635.928 cm
Therefore, the perimeter of the computer graphic is approximately 15635.928 cm.