Question

3-33. examine the rectangle at right.
a. write an expression for the perimeter in terms of x.
b. assuming the perimeter is 78 cm, determine the dimensions of the rectangle. show all of your work.
c. verify that the area of this rectangle is 360 sq. cm. explain how you know this.
3-34. write an equation for the tile pattern represented at right.
3-35. the kittis hog - nosed bat, or bumblebee bat, is one of the worlds smallest mammals. it typically weighs about 2×10^(-3) kilograms and has a 1.5×10^(-1) meter wingspan. a giant golden - crowned flying fox bat, on the other hand, typically weighs 1.6 kilograms and has a wingspan of up to 1.7 meters. estimate about how many times heavier a flying fox bat is than a bumblebee bat, without using a calculator.
3-36. perform the indicated operations.
a. -3 2/9 + 8 7/9
b. -7 2/7 - 4 1/5
c. 1 5/7·3 6/7
d. -8 1/7÷ - 5 5/9

Explanation:

3 - 33

a.

Step1: Recall perimeter formula

The perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Here, $l = 2x$ and $w=x + 3$.
$P=2(2x+(x + 3))$

Step2: Simplify the expression

First, simplify the expression inside the parentheses: $2x+(x + 3)=3x + 3$. Then, multiply by 2: $P = 2(3x + 3)=6x+6$.

Step1: Set up the equation

We know that $P=6x + 6$ and $P = 78$. So, set up the equation $6x+6=78$.

Step2: Solve for $x$

Subtract 6 from both sides: $6x=78 - 6=72$. Then divide both sides by 6: $x=\frac{72}{6}=12$.

Step3: Find the dimensions

The length $l = 2x$, substituting $x = 12$, we get $l=2\times12 = 24$ cm. The width $w=x + 3$, substituting $x = 12$, we get $w=12+3=15$ cm.

Step1: Recall area formula

The area $A$ of a rectangle is $A=l\times w$. Here, $l = 24$ cm and $w = 15$ cm.
$A=24\times15$

Step2: Calculate the area

$24\times15=(20 + 4)\times15=20\times15+4\times15=300+60 = 360$ sq.cm. Since the product of the length and width is 360 sq.cm, the area of the rectangle is 360 sq.cm.

Answer:

$6x + 6$

b.