Answer:
Length: 15 inches
Width: 3 inches
Step-by-step explanation:
Let'
L ----> the length of the model in inches
W ---> the width of the model in inches
we know that
The area of the model is given by the formula
[tex]A=LW[/tex]
we have
[tex]A=45\ in^2[/tex]
so
[tex]45=LW[/tex] ----> equation A
Remember that
the width is 12 inches less than the length
so
[tex]W=L-12[/tex] ---> equation B
substitute equation B in equation A
[tex]45=L(L-12)[/tex]
solve for L
[tex]45=L^2-12L[/tex]
[tex]L^2-12L-45=0[/tex]
Solve the quadratic equation by graphing
using a graphing tool
The solution is L=15 in
see the attached figure
Find the value of W
[tex]W=L-12[/tex]
substitute the value of L
[tex]W=15-12=3\ in[/tex]
therefore
The dimensions of the model are
Length: 15 inches
Width: 3 inches
