Question

using your math

1. the area of a rectangle is 18 square centimeters. if the length and width are both whole numbers, list all possible values for the length and width (assuming the length is the longer side). draw each rectangle.
2. a rectangle has an area of 11 square inches. if its length and width are both whole numbers, what is the perimeter of this rectangle in units of inches? remember: perimeter is the total length that surrounds a figure. show how you found your answer.

reviewing your math

1. what is the least common multiple of 6 and 10?
2. evaluate each of the following:

(a) $\frac{52}{7}$
(b) $8enclose{longdiv}{184}$

1. donna has 32 cards in her deck which is four times as many as laura has. if laura adds six cards to her deck, how many will she have? justify your answer.

Explanation:

4.

Step1: Recall area formula

$A = l\times w$, where $A = 18$ and $l\geq w$, $l,w\in\mathbb{Z}$.

Step2: Find factor - pairs

$18=18\times1$, $18 = 9\times2$, $18=6\times3$.

Step1: Find factor - pairs

Since $A = l\times w=11$ and $l,w\in\mathbb{Z}$, then $l = 11$, $w = 1$.

Step2: Calculate perimeter

$P=2(l + w)=2(11 + 1)=24$ inches.

Step1: Prime - factorize

$6 = 2\times3$, $10=2\times5$.

Step2: Find LCM

$LCM(6,10)=2\times3\times5 = 30$.

Answer:

Length: 18 cm, Width: 1 cm; Length: 9 cm, Width: 2 cm; Length: 6 cm, Width: 3 cm

5.