Kyle W.

asked • 02/22/18

Quadratic equations

Question; The width of a rectangle is 7 meters greater than its length. If the rectangle is 170 square meters, write the quadratic equation in standard form for the equation taht would represent the area of the rectangle. Let x equal the length of the rectangle

1 Expert Answer

By:

Brittany D. answered • 02/22/18

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Elementary-College Tutor Specializing in Science, Math & Writing

Brittany D.

Area of a rectangle = length(L) x width(w), where the area is reported in "units2" (in this case, it would be meters2).

The problem tells us that:
1) w = L + 7m

2) area of rectangle= 170m2

First, try writing an equation to represent the area of the rectangle using variables for length and width:

170m2= w + L

Then, substitute "w" for the equation given for width. This allows you to only have one variable (L) to be solved for in the equation:

170m2 = (L + 7m) + L

Use order of operations to combine like terms:

170m2 = L + 7m + L
170m2 = 1L + 7m + 1L
170m2 = ?L + 7m

Standard form of a quadratic equation is:

ax2 + bx + c= 0

*Note: In this case, the "x" represents units. Do not get it confused with the "x" that equals the length in the problem. If it would make it easier to visualize, substitute the "x" in the standard form above, with the units being used in the problem; in this case, meters ("m").

am2 + bm + c = 0

That means, all variables need to be moved to one side, so that they can be equal to 0. This will allow you to arrange each term into standard form (which would further allow you to then solve for the variable, if the question asked). In this case:

170m2 = ?L + 7m
-170m2 = -170m2
0 = ?L + 7m -170m2

At this point, it may help to identify which values in the problem represent each value of the standard form:

am2 = area of rectangle =
bm = width =
c = length =

Now, just re-arrange those values into standard form, where "am2" = area of rectangle; "bm" = width; and "c" = length. Once re-arranged into standard form, DO NOT forget to change the length "L" variable to "x" in your final answer! (Since the question asked for "x" to equal the length in the final answer.)

*Note: Remember, for the quadratic equation to be in standard form, it needs to have all variables on one side and be set to equal 0.
Report

02/23/18

Brittany D.

One more edit:
 
Where it says:
"At this point, it may help to identify which values in the problem represent each value of the standard form," it should read:

am2 = area of rectangle =
bm =         
c =

Now, just re-arrange those values into standard form, and remember to make sure each term is written with the correct sign in front of it. Once re-arranged to the correct form, DO NOT forget to change the length "L" variable to "x" in your final answer! (Since the question asked for "x" to equal the length in the final answer.)

*Note: Remember, for the quadratic equation to be in standard form, it needs to have all variables on one side and be set to equal 0.
Report

02/23/18

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