Answer:
W = 10 cm
Step-by-step explanation:
Area of a Triangle and a Rectangle
The area of a triangle of base B and height H is:
[tex]\displaystyle A_t=\frac{BH}{2}[/tex]
The area of a rectangle of width W and length L is:
[tex]A_r=WL[/tex]
We are given the base of the triangle B=6 cm and the height H=8 cm, thus the area is:
[tex]\displaystyle A_t=\frac{6*8}{2}= 24\ cm^2[/tex]
The area of the rectangle is 5 times the area of the triangle, thus:
[tex]A_r=5*24\ cm^2=120\ cm^2[/tex]
If we know the area of the rectangle and its length, we can find the width by solving for W:
[tex]\displaystyle W=\frac{A_r}{L}[/tex]
The rectangle has a length of L=12 cm, thus:
[tex]\displaystyle W=\frac{120}{12}=10\ cm[/tex]
W = 10 cm
