Answer:
Length= 72 ft.
Step-by-step explanation:
The area of a rectangle is found by multiplying the width by the length. The problem tell us that the result of that operation is 4,320 ft^2 and that the ratio of length to the width is 6:5.
We can create 2 expressions with this information.
Let "w" be the width if the rectangle.
Let "l" be the length of the rectangle.
Expresion 1. [tex]l*w = 4,320[/tex].
Expresion 2. = [tex]\frac{l}{w} =\frac{6}{5}[/tex].
To find the values of "l" and "w", we have to solve the linear equation system formed by expression 1 and 2. Let's go ahead and solve it.
Step 1. Solve one of the expressions for one of the variables.
Let's solve expression 1 for l.
[tex]l*w = 4,320\\ \\l = \frac{4,320}{w}[/tex]
Step 2. Take the value found for l in step 1 and substitute it for l in expression 2.
[tex]\frac{l}{w} =\frac{6}{5}\\ \\\frac{\frac{4,320}{w}}{w} =\frac{6}{5}[/tex]
Step 3. Solve for w.
[tex]\frac{\frac{4,320}{w} }{w}} =\frac{6}{5}\\ \\\frac{1}{w} * \frac{4320}{w} =\frac{6}{5}\\ \\ \frac{w^{2}}{4320 } =\frac{5}{6}\\ \\w^{2}=\frac{5}{6}*4320\\ \\w=\sqrt{\frac{5}{6}*4320} \\ \\w=60[/tex]
Step 4. Use the found value of w (60) and plug in into expression 1.
[tex]l*(60) = 4,320[/tex]
Step 5. Solve for l.
[tex]l*(60) = 4,320\\ \\l=\frac{4,320}{60} \\ \\l=72[/tex]
Express a result.
Length= 72 ft.
Width= 60 ft.
-------------------------------------------------------------------------------------------------------
Verification.
To verify the answers, take the values and plug them into both of the equations. If the results match the initial parameters, the answers are correct.
[tex](72)*(60) = 4320[/tex] Correct.
[tex]\frac{72}{60} =\frac{6}{5}[/tex] Correct.
The answers are correct.
