Question

In triangle ABC measure angle A =90, AB=6cm BC=10 cm.Find the area of triangle ABC also the length of altitude on hypotenuse.

Answer 1

from where did perpendicular drawn to hypotenus

Answer 2

Answer:

The Area of the triangle ABC is found to be 24 sq.cm with the altitude of the triangle being 8 cm.

Step-by-step explanation:

As one of the angle of the given triangle is given to be $90^\circ$, so, the triangle is a right angled triangle.

We know that the area of a right angled triangle is given by:

$A=\frac{1}{2}\times base\times height$

In this case, as the right angle is present on point A, so the base and height will be AB and AC,

We know the value of the sides AB and BC, thus using the Pythagoras Theorem, we get:

$BC^2=AB^2+AC^2$

Substituting the given values, we get:

$10^2=6^2+AC^2$

Simplifying it, we get:

$100-36=AC^2$

or we can say:

$AC^2=64=(8)^2$

So, we get:

$AC=8\ cm$

Thus, the length of altitude is found to be 8 cm.

Substituting AC and AB in the expression of Area, we get:

$A=\frac{1}{2}\times 8\times 6$

Simplifying it, we get:

$A=\frac{48}{2}$

or we can say:

$A=24\ cm^2$

Thus, the area of the given triangle is found to be 24 square cm.