The Perimeter of a right angled triangle is 40 CM. Find the area of the right angled triangle.
Some information is needed
To find the area of a right-angled triangle, we need to know the lengths of its two perpendicular sides. However, in this case, we are only given the perimeter of the triangle, which is the sum of all three sides.
Since it is a right-angled triangle, we can denote the two perpendicular sides as a and b, and the hypotenuse as c. From the given information, we can write the equation:
a + b + c = 40
In a right-angled triangle, the sum of the squares of the lengths of the two perpendicular sides is equal to the square of the length of the hypotenuse. This relationship is known as the Pythagorean theorem.
Using the Pythagorean theorem, we have:
a^2 + b^2 = c^2
Now we have two equations:
a + b + c = 40 -> Equation 1
a^2 + b^2 = c^2 -> Equation 2
We can solve these equations to find the sides of the triangle:
From Equation 1, we can isolate c:
c = 40 - a - b
Substituting this value of c into Equation 2:
a^2 + b^2 = (40 - a - b)^2
Expanding and simplifying:
a^2 + b^2 = 1600 - 80a - 80b + 2ab + a^2 + b^2
Rearranging the terms:
80a + 80b - 2ab = 1600
Dividing both sides by 2:
40a + 40b - ab = 800
Rearranging:
ab - 40a - 40b + 800 = 0
Now, we have a quadratic equation:
ab - 40a - 40b + 800 = 0
To solve this quadratic equation, there are multiple methods such as factoring, completing the square, or using the quadratic formula. However, since the problem doesn't mention the values of a or b, we cannot determine the exact values without additional information.
Hence, without more information or numerical values for sides a and b, we cannot find the area of the right-angled triangle.
Not enough information
c^2 = a^2 + b^2
P = a + b + c = 40
or
P = a + b + sqrt(a^2+b^2) = 40
now if it is isoceles, a = b, then
P = 2 a + sqrt (2 a^2) = 3.414 a = 40
A = (1/2) a b = (1/2)a^2 = (1/2)(40/3.414)^2
= 68.6