The hypote of a right triangle is square Root of 40
a: what whole number lenth of legs can this triangle have?
b: draw a Line segment that has the lenth of square Root of 40.
C: what is the area of this triangle?
Please explain with formula ans working...
a. side1^2 + side2^2 = hypotenuse^2
b. Cannot draw here
c. 1/2 side^2
a. 40 = 36+4
so, the legs are 2 and 6
To answer these questions, we need to understand the Pythagorean theorem and the formula for the area of a right triangle.
a) According to the Pythagorean theorem, the sum of the squares of the lengths of the legs (the two shorter sides) of a right triangle is equal to the square of the length of the hypotenuse (the longest side). In equation form, it is written as:
a^2 + b^2 = c^2
Where:
a and b are the lengths of the legs
c is the length of the hypotenuse
Given that the hypotenuse in this triangle has a length of √40, we can determine which whole number lengths the legs can have by finding the factors of 40 and checking if any of them satisfy the Pythagorean theorem. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.
Let's go through each factor to see which combinations of legs result in a right triangle:
For a = 1:
1^2 + b^2 = (√40)^2
1 + b^2 = 40
b^2 = 39 (which is not a perfect square)
For a = 2:
2^2 + b^2 = (√40)^2
4 + b^2 = 40
b^2 = 36
b = 6
Since b is a whole number (6), this combination results in a right triangle.
We can continue this process with other factors, but in this case, the only whole number lengths for the legs are a=2 and b=6.
b) To draw a line segment of length √40, you can follow these steps:
1. Start with a line segment.
2. Measure the length of √40 = 6.32 (approximately).
3. Using a ruler, mark a point at 6.32 units from the starting point.
4. Connect the two points to form the desired line segment.
c) To calculate the area of the right triangle, we can use the formula:
Area = (base * height) / 2
Since the legs of the right triangle are a = 2 and b = 6, we can assign a as the base and b as the height. Thus:
Area = (2 * 6) / 2
Area = 12 / 2
Area = 6 square units
Therefore, the area of this right triangle is 6 square units.