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

Answer:

$Base = 6cm$ and $Height = 12cm$

$Base = 4cm$ and $Height = 18cm$

$Base = 9cm$ and $Height = 8cm$

Step-by-step 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