Answer:
[tex]Base = 6cm[/tex] and [tex]Height = 12cm[/tex]
[tex]Base = 4cm[/tex] and [tex]Height = 18cm[/tex]
[tex]Base = 9cm[/tex] and [tex]Height = 8cm[/tex]
Step-by-step explanation:
Given
Shape: Triangle
[tex]Area = 36cm^2[/tex]
Solving (a): Three possible dimensions
The area of a triangle is:
[tex]Area = 0.5 * Base * Height[/tex]
Let: [tex]Base = 6cm[/tex]
So, we have:
[tex]36= 0.5 * 6* Height[/tex]
[tex]36= 3* Height[/tex]
Solve for Height
[tex]12 = Height[/tex]
[tex]Height = 12[/tex]
So, a possible dimension is: [tex]Base = 6cm[/tex] and [tex]Height = 12cm[/tex]
Let: [tex]Base = 4cm[/tex]
So, we have:
[tex]36= 0.5 * 4* Height[/tex]
[tex]36= 2* Height[/tex]
Solve for Height
[tex]18 = Height[/tex]
[tex]Height = 18[/tex]
So, a possible dimension is: [tex]Base = 4cm[/tex] and [tex]Height = 18cm[/tex]
Let: [tex]Base = 9cm[/tex]
So, we have:
[tex]36= 0.5 * 9* Height[/tex]
[tex]36= 4.5* Height[/tex]
Solve for Height
[tex]8 = Height[/tex]
[tex]Height = 8[/tex]
So, a possible dimension is: [tex]Base = 9cm[/tex] and [tex]Height = 8cm[/tex]
So, the three possible dimensions are:
[tex]Base = 6cm[/tex] and [tex]Height = 12cm[/tex]
[tex]Base = 4cm[/tex] and [tex]Height = 18cm[/tex]
[tex]Base = 9cm[/tex] and [tex]Height = 8cm[/tex]
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
