Okay the question is: What is the area of a right triangle whose perimeter is 36 and whose sides are x, x+ 3, and x+6?
So far I've gotten x= 9 but I don't know what the height is and I need to know that to get the area.
The two shorter sides of the triangle are the base and altitude, so area=x(x+3)
Perimeter=36=x+x+3+x+6 = 3x+9
so x=9. So area =9(9+3) or...
108
thanks!!
If x=9,then,9+9+3+9+6=36
To find the area of a right triangle, you need its base and height. In this case, you have the lengths of the three sides of the triangle, but you need to determine the value of x and then calculate the height.
Let's start by considering the perimeter of the triangle. The perimeter is the sum of all three sides, and in this case, it is given as 36. So we can write the equation:
x + (x + 3) + (x + 6) = 36
Now, let's solve this equation to find the value of x:
Combining like terms, we have:
3x + 9 = 36
Subtracting 9 from both sides, we get:
3x = 27
Dividing both sides by 3, the equation becomes:
x = 9
Now that we know x = 9, we can substitute this value back into the sides of the triangle to find their lengths. The sides of the triangle are x, x + 3, and x + 6, so substituting x = 9, we get:
Side 1: x = 9
Side 2: x + 3 = 9 + 3 = 12
Side 3: x + 6 = 9 + 6 = 15
Now, we have the lengths of the three sides: 9, 12, and 15. To find the height of the triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is 15, and the other two sides are 9 and 12. So we have:
15^2 = 9^2 + 12^2
Simplifying, we get:
225 = 81 + 144
225 = 225
Since this equation is true, we have confirmed that the triangle is indeed a right triangle.
Now, let's calculate the area of the triangle using the formula:
Area = (base * height) / 2
Since we know that the base is the side with length 9, and we just determined that the height is the side with length 12, we can calculate the area as follows:
Area = (9 * 12) / 2
= 108 / 2
= 54
So, the area of the right triangle is 54 square units.