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3 years ago

8

A rectangular poster is 10 inches longer than it is wide. If the area of the poster is 171 square inches, find the dimensions of

the poster.

1 answer:

aivan3 [116]3 years ago

4 0

Length= 19 inches
width= 9 inches

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I need help with #1 of this problem. It has writings on it because I just looked up the answer because I’m confused but I want t

belka [17]

In the figure below

1) Using the theorem of similar triangles (ΔBXY and ΔBAC),

$\frac{BX}{BA}=\frac{BY}{BC}=\frac{XY}{AC}$

Where

$\begin{gathered} BX=4 \\ BA=5 \\ BY=6 \\ BC\text{ = x} \end{gathered}$

Thus,

$\begin{gathered} \frac{4}{5}=\frac{6}{x} \\ \text{cross}-\text{multiply} \\ 4\times x=6\times5 \\ 4x=30 \\ \text{divide both sides by the coefficient of x, which is 4} \\ \text{thus,} \\ \frac{4x}{4}=\frac{30}{4} \\ x=7.5 \end{gathered}$

thus, BC = 7.5

2) BX = 9, BA = 15, BY = 15, YC = y

In the above diagram,

$\begin{gathered} BC=BY+YC \\ \Rightarrow BC=15\text{ + y} \end{gathered}$

Thus, from the theorem of similar triangles,

$\begin{gathered} \frac{BX}{BA}=\frac{BY}{BC}=\frac{XY}{AC} \\ \frac{9}{15}=\frac{15}{15+y} \end{gathered}$

solving for y, we have

$\begin{gathered} \frac{9}{15}=\frac{15}{15+y} \\ \text{cross}-\text{multiply} \\ 9(15+y)=15(15) \\ \text{open brackets} \\ 135+9y=225 \\ \text{collect like terms} \\ 9y\text{ = 225}-135 \\ 9y=90 \\ \text{divide both sides by the coefficient of y, which is 9} \\ \text{thus,} \\ \frac{9y}{9}=\frac{90}{9} \\ \Rightarrow y=10 \end{gathered}$

thus, YC = 10.

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1 year ago

What is the square root of 108 in simplified radical form?

Alenkinab [10]

$\sqrt{108}=\sqrt{36 \times 3}=\sqrt{36} \times \sqrt{3}=6 \times \sqrt{3}=\boxed{6\sqrt{3}}$

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3 years ago

If the expression is expanded, what is the coefficient of x?

Nana76 [90]

Answer:

Coefficient is equal to 12

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3 years ago

A swimming pool has a diameter of 24 feet. What is the minimum amount of fabric needed to cover the pool if the cover must hang

Alika [10]

Answer:

531.167 ft²

Step-by-step explanation:

Given data

Dimension of pool

Diameter =24ft

Radius =12ft

If the cover must hang by 1ft around, then the diameter is 26ft

Radius =13ft

Area of cover = πr²

Substitute

Area = 3.142*13²

Area =3.143*169

Area =531.167 ft²

Hence the minimum area is 531.167 ft²

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Denise collects stuffed animals. The number of stuffed animals in her collection, a, after n, number of years, can be described

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