Question

The area of a triangle is 36 cm square. Give three possible sets of dimensions for the triangle and explain whether or not you can also give the triangles' side length.

Answer 1

`Base = 6cm` and
`Height = 12cm`

`Base = 4cm` and
`Height = 18cm`

`Base = 9cm` and
`Height = 8cm`

Explanation:

Given

Shape: Triangle

`Area = 36cm^2`

Solving (a): Three possible dimensions

The area of a triangle is:

`Area = 0.5 * Base * Height`

Let:
`Base = 6cm`

So, we have:

`36= 0.5 * 6* Height`

`36= 3* Height`

Solve for Height

`12 = Height`

`Height = 12`

So, a possible dimension is:
`Base = 6cm` and
`Height = 12cm`

Let:
`Base = 4cm`

So, we have:

`36= 0.5 * 4* Height`

`36= 2* Height`

Solve for Height

`18 = Height`

`Height = 18`

So, a possible dimension is:
`Base = 4cm` and
`Height = 18cm`

Let:
`Base = 9cm`

So, we have:

`36= 0.5 * 9* Height`

`36= 4.5* Height`

Solve for Height

`8 = Height`

`Height = 8`

So, a possible dimension is:
`Base = 9cm` and
`Height = 8cm`

So, the three possible dimensions are:

`Base = 6cm` and
`Height = 12cm`

`Base = 4cm` and
`Height = 18cm`

`Base = 9cm` and
`Height = 8cm`

Solving (b): Can the side lengths be given

We can only determine the base and the height of the triangle, the third side length can not be determined using the available information