Question

the length of the side of the triangle are 10,24and 26 find its area and as well as height​

Answer 1

Lengths of sides of triangle = 10, 24, 26

These values can be written as following

26² = 24² + 10²

i.e, 10, 24, 26 are pythagorean triplets

So, the given triangle is a Right-Angled triangle

So, Hypotenuse = 26

Base(Height) = 10

Height(Base) = 24

$\boxed{\tt{Area\:of\:the\:triangle=\frac{1}{2}\times Base \times Height}}$

$= \frac{1}{2} \times 10 \times 24$

$= 10 \times 12$

$= 120 \: {units}^{2}$

Area of the triangle = 120 units²

Height = 10 or 24

So, area of the triangle is 120 units² and height is either 10 or 24.