CPM Homework Help : AC Problem 7-40

CPM Homework Banner

Home > AC > Chapter 7 > Lesson 7.1.4 > Problem 7-40

7-40.

Copy and complete these generic rectangles on your paper. Then write the area of each rectangle as a product of the length and width and as a sum of the parts.

Generic rectangle
left edge $6$
interior left blank
interior right blank
bottom edge left $13x$
bottom edge right $-21$

Hint (a):
To write the area as a sum:

Find the area of each of the rectangle's sections. Then, add them together.
More Help (a):
To write the area as a product:

Multiply the total length by the total width, but don't simplify it.
Answer (a):
As a sum: $78x−126$
As a product: $6(13x−21)$

Generic rectangle left edge top $x$
interior top left blank
interior top right blank
left edge bottom $-5$
interior bottom left blank
interior bottom right blank
bottom edge left $x$
bottom edge right $+3$

Hint (b):
See the help for part (a).
Answer (b):
As a sum: $x^2−2x−15$
As a product: $(x−5)(x+3)$

Generic rectangle interior left $16x^2$
interior middle $-24x$
interior right $4$

Hint (c):
Find the greatest common factor of the areas. That will be the width. Then divide each area by the width to find the length. Then follow the steps for part (a).
More Help (c):
Generic rectangle
left edge $4$
interior left $16x^2$
interior middle $-24x$
interior right $4$
bottom edge left $4x^2$
bottom edge middle $-6x$
bottom edge right $1$

Generic rectangle
left edge top $3x$
interior top left blank
interior top right blank
left edge bottom $-2$
interior bottom left blank
interior bottom right blank
bottom edge left $x$
bottom edge right $+4$

Hint (d):
See the help for part (b).

© 2022 CPM Educational Program. All rights reserved.