The longer diagonal of a rhombus is 2 times as long as the shorter diagonal. Find the length of the shorter diagonal if the area is 24in squared.
Why did the clown go to math class? Because he heard there would be lots of "fun"damental concepts.
Let's solve this math problem using humor and math!
Let's say the length of the shorter diagonal is "x". Since the longer diagonal is 2 times as long as the shorter diagonal, we can say the length of the longer diagonal is "2x".
The area of a rhombus is given by the formula A = (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals.
In this case, we know that the area is 24in squared, so we have:
24 = (x * 2x) / 2
Simplifying the equation, we get:
24 = x^2
Now we can solve for x by taking the square root of both sides:
√24 = √x^2
Simplifying:
√(4 * 6) = x
2√6 = x
So, the length of the shorter diagonal is 2√6 inches.
If you need any further assistance, just clown around and ask me!
Let's assume that the length of the shorter diagonal is x inches.
Given that the longer diagonal is 2 times as long as the shorter diagonal, we can say that the length of the longer diagonal is 2x inches.
The area of a rhombus can be calculated using the formula: Area = (1/2) * d1 * d2, where d1 and d2 are the lengths of the diagonals.
Given that the area is 24 square inches, we can write the equation as:
24 = (1/2) * x * 2x
Simplifying the equation:
24 = x^2
To solve for x, we take the square root of both sides:
√(24) = √(x^2)
±√(24) = x
Since the length of the diagonal cannot be negative, we take the positive square root:
x = √24
Using a calculator, we find that √24 is approximately 4.899.
Therefore, the length of the shorter diagonal is approximately 4.899 inches.
To solve this problem, we can use the properties of a rhombus and the formula for the area of a rhombus.
1. Let's define the length of the shorter diagonal as "d" inches. Since the longer diagonal is 2 times as long as the shorter diagonal, the length of the longer diagonal would be 2d inches.
2. The formula for the area of a rhombus is A = (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals.
3. We are given that the area of the rhombus is 24 square inches. Substituting the values into the formula, we get: 24 = (d * 2d) / 2.
4. Simplifying the equation, we have: 24 = d^2.
5. To solve for d, we take the square root of both sides of the equation: √24 = √d^2. This gives us: √24 = d.
6. Therefore, the length of the shorter diagonal is approximately 4.9 inches (rounded to one decimal place).
So, the length of the shorter diagonal is approximately 4.9 inches when the area of the rhombus is 24 square inches.
The area of a rhomus is (1/2) the product of their diagonals
http://www.mathsteacher.com.au/year8/ch12_area/05_rhombus/rhombus.htm
so let one diagonal be x, the other be 2x
x(2x) = 24
2x^2 = 24
x^2 = 12
x = √12 = 2√3
form your conclusions.