Triangle abc is right angled at a .ad is drawn perpendicular to bc .if ab=5cm and ac=12cm find the area or triangle abc. Also find the length of ad
To find the area of triangle ABC, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
We know that triangle ABC is a right-angled triangle with AB as the base and AC as the height. Therefore, we can substitute the values into the formula:
Area = (1/2) * AB * AC
Given that AB = 5 cm and AC = 12 cm, we can calculate the area:
Area = (1/2) * 5 cm * 12 cm
= 30 cm²
So, the area of triangle ABC is 30 cm².
Now, to find the length of AD, we can use the Pythagorean theorem. 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 triangle ABC, AC is the hypotenuse and AD and CD are the other two sides. Therefore, we can use the formula:
AC² = AD² + CD²
Given that AC = 12 cm, we can substitute the values and solve for AD:
12² = AD² + CD²
144 = AD² + CD²
Since AD is the perpendicular or height with respect to base BC, it is equal to the length of BC, so we can write:
144 = AD² + BC²
Substituting the values, we get:
144 = AD² + 5²
144 = AD² + 25
Rearranging the equation, we have:
AD² = 144 - 25
AD² = 119
To solve for AD, we take the square root of both sides:
AD = √119
Therefore, the length of AD is approximately 10.92 cm (rounded to two decimal places).
area = (1/2)12*5 = 30
hypotenuse BC = 13
the area = 30 = (1/2)13*AD
AD =60/13