Answer:
The height and base of the rectangle are approximately 5.453 inches and 10.453 inches, respectively.
Step-by-step explanation:
From Geometry we remember that area of a rectangle ([tex]A[/tex]), measured in square inches, is equal to:
[tex]A = w \cdot h[/tex] (Eq. 1)
Where:
[tex]w[/tex] - Width, measured in inches.
[tex]h[/tex] - Height, measured in inches.
In addition, we get the following relationship from statement:
[tex]w = h+5\,in[/tex] (Eq. 2)
If we know that [tex]A = 57\,in^{2}[/tex], then the height of the rectangle is:
[tex]57\,in^{2} = (h+5\,in)\cdot h[/tex]
[tex]h^{2}+5\cdot h -57 = 0[/tex]
From Quadratic Formula we obtain the following roots:
[tex]h_{1} \approx 5.453\,in[/tex] and [tex]h_{2}\approx -10.453\,in[/tex]
Only the first root offers a reasonable solution, as length has always positive values. Thus, the height of the rectangle is approximately 5.453 inches.
Now we calculate the width of the rectangle from (Eq. 1):
[tex]w = \frac{A}{h}[/tex]
If we know that [tex]A = 57\,in^{2}[/tex] and [tex]h \approx 5.453 \,in[/tex], then the width of the rectangle is:
[tex]w = \frac{57\,in^{2}}{5.453\,in}[/tex]
[tex]w \approx 10.453\,in[/tex]
The height and base of the rectangle are approximately 5.453 inches and 10.453 inches, respectively.
