Triangle ABCis right angled at a .AD is perpendicular to BC.If AB=5cm,BC=13cm and AC=12cm,Find the area of triangle abc .Aiso findthe length of AD.
I hope you can figure the area of ABC with no trouble.
Using similar triangles, because angle B is the same in both, and both are right triangles,
12/13 = AD/5
AD = 60/13
Base of the triangle =13cm
altitude of the triangle=12cm
Area of the triangle=1/2(b)(a)
' =1/2(5)(12)
=30cm2
60/13AD and 30cm2triangle of ABC.
To find the area of triangle ABC, we can use the formula:
Area = (1/2) * base * height
Since triangle ABC is a right-angled triangle, we can use the lengths of the sides AB and AC as the base and height, respectively.
Area = (1/2) * AB * AC
Area = (1/2) * 5cm * 12cm
Area = 30cm²
Now, to find the length of AD, we can use the Pythagorean theorem. In a right-angled triangle, the square of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC).
AC² = AB² + BC²
Substituting the given values:
12cm² = 5cm² + 13cm²
144cm² = 25cm² + 169cm²
144cm² = 194cm²
We can subtract 25cm² from both sides:
144cm² - 25cm² = 194cm² - 25cm²
119cm² = 169cm²
To find the length of AD, we take the square root of both sides:
√119cm² = √169cm²
AD = √119cm
Therefore, the area of triangle ABC is 30cm², and the length of AD is approximately 10.92cm.