Triangle has an area of 46 square centimeters what is the measurement of the base One side is 11 cm and the other side is 9 cm
To find the base of the triangle, we can use the formula for the area of a triangle:
Area = (base * height) / 2
Given that the area of the triangle is 46 square centimeters, one side is 11 cm, and the other side is 9 cm, we can set up the following equation:
46 = (base * height) / 2
Since we do not know the height, we cannot solve for the base directly. However, we can use the Pythagorean theorem to find the height of the triangle.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the base and height form the two sides of the right-angled triangle.
So, we have:
height^2 = 11^2 - 9^2
height^2 = 121 - 81
height^2 = 40
height = sqrt(40)
height = 6.32 cm
Now that we have found the height of the triangle, we can substitute this value back into the area formula and solve for the base:
46 = (base * 6.32) / 2
46 = 3.16 * base
base = 46 / 3.16
base = 14.56 cm
Therefore, the measurement of the base of the triangle is approximately 14.56 cm.