The perimeter of a triangle ABC is 58cm.The base of the right triangle is 17 cm. What is th area of the right triangle and how do you figure it out?
With TrianCal (Online triangle solver) area is ≈ 144.2926829268 cm.
To find the area of a right triangle, you need to know the lengths of both of its legs or at least one length of a leg and the hypotenuse. However, in this case, only the base of the right triangle is provided. To proceed, we need further information.
To find the area of a right triangle, we need to know the lengths of both of its legs or the length of one leg and the length of the hypotenuse. In this case, we are given the base of the triangle, which is one of the legs.
Let's assume that the other leg has a length of "a" cm and the hypotenuse has a length of "b" cm.
The perimeter of a triangle is equal to the sum of the lengths of its three sides. In this case, we are given that the perimeter is 58 cm, so we can set up an equation:
17 cm + a + b = 58 cm
Rearranging the equation, we have:
a + b = 58 cm - 17 cm
a + b = 41 cm
Since it's a right triangle, we can use the Pythagorean theorem to relate the lengths of the legs and the hypotenuse:
a^2 + b^2 = c^2 (where c is the length of the hypotenuse)
We know the length of one leg is 17 cm, so we substitute this into the equation:
17^2 + b^2 = c^2
289 + b^2 = c^2
Now, we have two equations:
a + b = 41 cm
289 + b^2 = c^2
To solve for the area, we need to find the lengths of both legs. From the first equation, we can solve for a in terms of b:
a = 41 cm - b
Substituting this into the second equation:
289 + b^2 = c^2
We can now find the area of the right triangle by using the formula:
Area = (base * height) / 2
In this case, the base is 17 cm, and we need to find the height, which is the other leg (a) in our case. Substituting the values we found:
Area = (17 cm * (41 cm - b)) / 2
Simplifying the expression:
Area = (17 cm * 41 cm - 17 cm * b) / 2
Area = (697 cm^2 - 17 cm * b) / 2
Therefore, the area of the right triangle can be found by substituting the value of b and evaluating the expression.