Answer:
The red material needed is [tex]84\ in^{2}[/tex]
The white material needed is [tex]84\ in^{2}[/tex]
The blue material needed is [tex]48\ in^{2}[/tex]
Step-by-step explanation:
Let
x------> area of the red material
y-----> area of the white
z----> area of the blue material
The total area is equal to
[tex]A=(18)(12)=216\ in^{2}[/tex]
so
[tex]x+y+z=216[/tex] -------> equation A
The area of the white is equal to the area of the red
so
[tex]x=y[/tex] ------> equation B
Find the area of the triangular blue material
[tex]z=\frac{1}{2}(12)(18-10)=48\ in^{2}[/tex] -----> equation C
substitute equation C and equation B in equation A
[tex]y+y+48=216[/tex]
[tex]2y=216-48[/tex]
[tex]y=168/2=84\ in^{2}[/tex]
Find the value of x
[tex]x=84\ in^{2}[/tex]
Therefore
The area of the red material is [tex]84\ in^{2}[/tex]
The area of the white material is [tex]84\ in^{2}[/tex]
The area of the blue material is [tex]48\ in^{2}[/tex]
