The area of a triangle whose legs are in the ratio of 2:3 is 48. The length of the hypotenuse is
a. square root 13
b. 8
c. 2 square root 52
d. 12
e. 208
please answer and explain
I assume it is a right triangle.
Area = 48 = 1/2 hb
96 = hb
Set one variable as multiple of 2 and see if the same multiple of 3 will multiply to = 96.
Pythagorean theorem:
8^2 + 12^2 = Hyp^2
64 + 144 = 208 = Hyp^2
√208 does not match any of your choices.
14 < √208 < 15.
Do you have any typos? Did you omit the square root symbol from the last choice?
that is my homewrok, i didn't omit the square root symbol from the last choice
e. 208
or, look at it as a scaling problem.
In a right triangle with legs 2 and 3, the hypotenuse is √13, and the area is (1/2)(2)(3) = 3.
Your triangle has a an of 48, which is 16*3
Since the area scales as the square of the scale factor, the hypotenuse is 4*√13 = 2√52
thank you
To answer this question, we can use the concept of similar triangles and the area formula of a triangle.
We are given that the legs of the triangle are in the ratio of 2:3. Let's assume that the length of the two legs are 2x and 3x, respectively.
Now, we know that the area of a triangle is given by the formula: Area = (base * height) / 2.
Since the legs of the triangle form a right angle, one of the legs can be considered the base and the other leg can be considered the height. Let's assume that the shorter leg (2x) is the base, and the longer leg (3x) is the height.
So, the area of the triangle can be written as: 48 = (2x * 3x) / 2.
Simplifying this equation, we get: 48 = 3x^2.
Now, let's solve for x. Dividing both sides of the equation by 3, we get: x^2 = 16.
Taking the square root of both sides, we find: x = 4.
Now that we know the value of x, we can find the lengths of the legs of the triangle. The shorter leg is 2x = 2 * 4 = 8, and the longer leg is 3x = 3 * 4 = 12.
Finally, to find the length of the hypotenuse, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
So, the hypotenuse can be found using the equation: hypotenuse^2 = 8^2 + 12^2.
Calculating this, we have: hypotenuse^2 = 64 + 144 = 208.
Taking the square root of both sides, we get: hypotenuse ≈ √208.
Therefore, the length of the hypotenuse is approximately √208.
Hence, the correct answer is option c) √208.