the the length of a rectangle is 2 cm less than three times its width. its area is 21 cm. find the dimensions of rectangle.

The width is ? ,

the length is ?

thanks

the the length of a rectangle is 2 cm less than three times its width. its area is 21 cm. find the dimensions of rectangle.

The width is ? ,

the length is ?

thanks

Tutors, please sign in to answer this question.

Let W represent the width of the rectangle and L represent the length of the rectangle. That is,

width = W and length = L

We are given that the length (L) is 2 cm less than 3 times the width (W). From this, we arrive at the following:

L = 3W - 2

We are also given that the area (A) of the rectangle is 21 cm^{2}. Since the area of a rectangle is the product of the rectangle's width and the length, then we have the following:

area = A = 21 cm^{2}

A = W•L ==> 21 = W•(3W - 2)

Distributing the W into each term inside the parentheses we get the following:

21 = W•3W - W•2

21 = 3W^{2} - 2W

Subtracting 21 from both sides of the equation yields the following quadratic equation:

3W^{2} - 2W - 21 = 0

Solve by factoring the left hand side of the above equation:

(3W + 7)(W - 3) = 0

By the zero product property we can set each binomial equal to 0 and solve for W in each:

3W + 7 = 0 and W - 3 = 0

3W = -7 W = 3

W = -7/3

Since the width cannot be negative, we omit the negative answer and only consider the positive answer. That is, the width (W) of the rectangle is equal to 3 cm.

Since the length (L) of the rectangle is 2 cm less than 3 times the width, then the length of determined by using the expression we found for L:

L = 3W - 2 = 3(3) - 2 = 9 - 2 = 7

Thus, the length of the rectangle is 7 cm.

Hey Motammem -- sometimes an "eyeball" approach works:

Begin with focus on the simplest part of the problem ... Area is 21 ... probably 3x7

Finally check 3(3) is 2 bigger than 7 ... Very best wishes :)

Jennifer C.

Experienced Educator Specializing in Test Prep and Enrichment

Brooklyn, NY

5.0
(70 ratings)

David T.

Very Experienced, Knowledgeable, and Patient Math Tutor

Dobbs Ferry, NY

5.0
(93 ratings)

Sean B.

Premier NYC Math tutor - young, passionate and talented

New York, NY

4.8
(30 ratings)