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Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728

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BuyFindarrow_forward

Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728
Textbook Problem

Problem Set 3.3

For Problems 85-89, use geometry to solve the problems. (Objective 5)

 Explain how Figure 3.16 can be used to demonstrate geometrically that x + 7 x - 3 = x 2 + 4 x - 21 .

To determine

To find:

To demonstrate geometrically the indicated product of the given expression.

Explanation

The figure given below depicts the dimension of the rectangles.

The length and width of the shaded part of the rectangle are x-3 and x+7 respectively.

Area of a rectangle whose length and width are l and w is:

A=lw

So,

A=x-3x+7... 1

Let A1 represent the area of the upper part of the shaded rectangle.

Therefore, area of the shaded rectangle with length x-3 and width x is:

A1=x-3x=x2-3x

Let A2 represent the area of the lower part of the shaded rectangle.

The length and width of the lower part of shaded rectangle are x-3 and 7 respectively.

Therefore, area of the shaded rectangle with length x-3 and width 7 is:

A2=x-37=7x-21

Area of the shaded part of the rectangle is the sum of the upper and lower parts of the shaded rectangle

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