Right triangle ABC has one leg of length 12 in and a hypotenuse of length 13 inch.
A) Determine the length of the other leg
B) Determine the perimeter of the triangle.
C)Determine the area of the triangle.
Must show work as well as answers for each of the above.
learn to recognize common triangles. 5-12-13 is one of them.
Now everything should be easy. Come back if not.
Might as well show your work while you're at it . . .
To find the length of the other leg of the right triangle, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's label the unknown leg as "b".
According to the Pythagorean theorem, we have the equation: a^2 + b^2 = c^2
Substituting the known values, we have: 12^2 + b^2 = 13^2
Simplifying the equation, we get: 144 + b^2 = 169
Subtracting 144 from both sides, we have: b^2 = 25
Taking the square root of both sides, we get: b = 5
So, the length of the other leg of the right triangle is 5 inches.
To determine the perimeter of the triangle, we can add up the lengths of all three sides.
The perimeter is given by: Perimeter = a + b + c
Substituting the known values, we have: Perimeter = 12 + 5 + 13
Simplifying the equation, we get: Perimeter = 30
So, the perimeter of the triangle is 30 inches.
To determine the area of the triangle, we can use the formula: Area = 1/2 * base * height
In this case, the base and height are given by the lengths of the two legs of the right triangle.
The area is given by: Area = 1/2 * a * b
Substituting the known values, we have: Area = 1/2 * 12 * 5
Simplifying the equation, we get: Area = 30
So, the area of the triangle is 30 square inches.