in a adjoining figure,CAB is right angled triangle where AC=4cm(height),AB =3cm(base),and BC=5cm (hypotenuse),and AD is a altitude from BC .then find the length of altitude from A toBC,if its area is 6cm square.
of course the area of ABC = (1/2)(3*4) = 6 :)
also
(1/2)(AD)(5) = 6
AD = 12/5 = 2.4 cm
To find the length of the altitude from point A to BC, we'll start by calculating the area of the right-angled triangle CAB using the given base and height.
The area of a triangle is given by the formula A = (1/2) * base * height.
In this case, the base (AB) is 3cm and the height (AC) is 4cm. So, plugging these values into the formula, we get:
A = (1/2) * 3cm * 4cm
A = 6cm^2
Now, we have the area of the triangle as 6cm^2.
Next, let's calculate the length of AD, which is the altitude from BC. We know that the area of a triangle is given by the formula:
A = (1/2) * base * height
In this case, the base (BC) is 5cm and the height (AD) is unknown. We can rearrange the formula to solve for the height:
height = (2 * A) / base
Plugging in the values, we get:
height = (2 * 6cm^2) / 5cm
height = 12cm^2 / 5cm
height = 2.4cm
Therefore, the length of the altitude from point A to BC is 2.4cm.