Question

The area of a right angled triangle is 140. If the base is 28, what’s the height and perimeter?

Answer 1

The given area of the right triangle is 140

The base of the right triangle is 28

Using the formula for area of triangle,

`A=(1)/(2)bh`

It follows:

`140=(1)/(2)*28* h`

Solve for h

This gives

`\begin{gathered} 140=14h \\ h=(140)/(14) \\ h=10 \end{gathered}`

Therefore the height of the right triangle is 10 units

To find the perimeter the third side of the right triangle will be found using pythagoras theorem

Let the length side be x

Notice that the third side is the hypotenuse, it follows

`\begin{gathered} x^2=28^2+10^2 \\ x=√(884) \end{gathered}`

Therefore the perimeter is

`\begin{gathered} P=28+10+√(884) \\ P=38+√(4*221) \\ P=38+2√(221) \end{gathered}`

Therefore the perimeter is:

`P=38+2√(221)`