the base of right angled triangle measures 48 cm and its hypotenuse is 50 cm. find the area of triangle
50^2 - 48^2 = 196
square root of 196 = 14
adjacent side = 14cm
To find the area of a right-angled triangle, we can use the formula:
Area = (1/2) * base * height
In this case, the base of the triangle is given as 48 cm. We still need to find the height.
We can use the Pythagorean theorem to find the height. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Mathematically, it is expressed as:
c^2 = a^2 + b^2
where c is the hypotenuse, and a and b are the other two sides.
In this case, the hypotenuse is given as 50 cm, and the base (a) is given as 48 cm.
Plugging in these values into the formula, we get:
50^2 = 48^2 + b^2
Simplifying this equation gives us:
2500 = 2304 + b^2
Subtracting 2304 from both sides gives us:
196 = b^2
Taking the square root of both sides, we find:
b = √196
b = 14 cm
Now that we have the base (48 cm) and height (14 cm), we can calculate the area using the formula:
Area = (1/2) * base * height
Plugging in the values, we get:
Area = (1/2) * 48 * 14
Area = (24) * 14
Area = 336 cm^2
Therefore, the area of the right-angled triangle is 336 square cm.