Question

The area of a rectangle is 4,320 ft2. The ratio of the length to the width is 6:5. Find the length of the rectangle.

A. 12 ft
B. 60 ft
C.
72 ft
D. 132 ft

Answer 1

Length= 72 ft.

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.
`l*w = 4,320`.

Expresion 2. =
`(l)/(w) =(6)/(5)`.

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.

`l*w = 4,320\\ \\l = (4,320)/(w)`

Step 2. Take the value found for l in step 1 and substitute it for l in expression 2.

`(l)/(w) =(6)/(5)\\ \\((4,320)/(w))/(w) =(6)/(5)`

Step 3. Solve for w.

`((4,320)/(w) )/(w)} =(6)/(5)\\ \\(1)/(w) * (4320)/(w) =(6)/(5)\\ \\ (w^(2))/(4320 ) =(5)/(6)\\ \\w^(2)=(5)/(6)*4320\\ \\w=\sqrt{(5)/(6)*4320} \\ \\w=60`

Step 4. Use the found value of w (60) and plug in into expression 1.

`l*(60) = 4,320`

Step 5. Solve for l.

`l*(60) = 4,320\\ \\l=(4,320)/(60) \\ \\l=72`

Express a result.

Length= 72 ft.

Width= 60 ft.

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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.

`(72)*(60) = 4320` Correct.

`(72)/(60) =(6)/(5)` Correct.

The answers are correct.