Triangle ABC is a right angled at A. AD is perpendicular to BC,AB=5cm,BC=13cm andAC=12cm. Find the area of triangle ABC.also find the length of AD
You will have 3 similar right-angled triangles.
I will list them with matching vertices
ABC
DBA
DAC
You can now form any ratio
e.g. BC/AB = BA/DB = AC/DA
plug in your given values and you can find all sides
To find the area of triangle ABC, we can use the formula:
Area = (1/2) * base * height
In this case, the base could be AB or BC, and the height would be the perpendicular distance from the base to the opposite vertex.
Since triangle ABC is a right-angled triangle, base AB can be chosen. So, the area of triangle ABC is:
Area = (1/2) * AB * AD
To find the value of AD, we can use Pythagoras' theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Applying Pythagoras' theorem, we have:
AC^2 = AB^2 + BC^2
12^2 = 5^2 + 13^2
144 = 25 + 169
144 = 194
This equation is not true. Hence, there seems to be an error in the given lengths of the sides of the triangle. Please double-check the values provided for AB, BC, and AC, as the given triangle dimensions do not form a right-angled triangle.