Question

show that the sides 5cm,12cm,13cm,make a right angle triangle.find the length of the altitude on the longest side.​

Answer 1

Answer:

yes the triangle given over here is right angled triangle as the square of the longest side is equal to the sum of squares of the other two sides. now, by construction draw an altitude on the longest side. we will be taking the hypotenuse the base as the altitude is drawn from it.

Answer 2

Given, sides of triangle 5 cm, 12 cm, 13 cm.

Now semi perimeter, s = 

$\frac{sum of the sides of triangle}{2}$

$= \frac{15 + 12 + 13}{2} = 15cm$

Using heron's formula, Area of triangle =

$\sqrt{s(s -a )(s - b)(s - c)}$

$= \sqrt{15(15 - 5)(15 - 12)(15 - 13)}$

$= \sqrt{15 \times 10 \times 3 \times 2 } = 30$

Using altitude, area of triangle =½×base×altitude=30cm²

½×13× altitude =30

$= altitude = \frac{30 \times 2}{13} = 4.61cm$

So, altitude corresponding to largest side is 4.61 cm.