Question

an isosceles triangle has congruent sides of 20cm. the base is 10cm. find the height of the triangle.​

Answer 1

`\large\boxed{A_\triangle=25√(15)\ cm^2}`

Explanation:

Look at the picture.

The formula of an area of a triangle:

`A_\triangle=(bh)/(2)`

b - base

h - height

We need a length of a height.

Use the Pythagorean theorem:

`leg^2+leg^2=hypotenuse^2`

We have:

`leg=5,\ leg=h,\ hypotenuse=20`

Substitute:

`5^2+h^2=20^2`

`25+h^2=400` subtract 25 from both sides

`h^2=375\to h=√(375)\\\\h=√((25)(15))\\\\h=√(25)\cdot√(15)\\\\h=5√(15)\ cm`

Calculate the area:

`A_\triangle=((10)(5√(15)))/(2)=(50√(15))/(2)=25√(15)\ cm^2`