# Geometry Concepts

*label*Mathematics

*timer*Asked: Apr 26th, 2017

*account_balance_wallet*$10

### Question Description

1. A label on an iced tea drink mix says to use 2 tbsp of iced tea mix to make one serving (8 oz) of iced tea.

a. What is the ratio of drink mix to iced tea? (Hint: 1 oz = 2 tbsp)

b. Suppose you want to make a quart (32 oz) of iced tea. How many ounces of drink mix should be used?

c. How many tablespoons of iced tea mix should be used to make a quart (32 oz) of iced tea?

2. △ RST has coordinates R(-4, -3), S(0, 5), and T(7, -3).

a. Graph △ RST in a coordinate plane.

b. Find the perimeter of △ RST.

c. Find the area of △ RST.

d. The centroid of a triangle is the intersection of its medians. Use the following steps to find the centroid of △ RST using segment partition.

i. Find the midpoint of . Label it N.

ii. Find the point, C, that partitions such that SC:CN has a ratio of 2:1 .

iii. Plot point C in your graph of △ RST.

e. Find and graph the midpoints of , ,and . Draw a segment connecting the vertex opposite each midpoint to the midpoint.

i. How does the intersection of the segments compare to point C from question 4?

3. Brian is renting an apartment. The floor plan of the apartment is shown below.

a. What is the total area of the apartment?

b. What are the dimensions of the master bedroom?

c. Brian wants to buy a dining room table from the local furniture store. He sees a table that is 9 ft long and 3 ft wide. Would it be reasonable to buy this table to put in the dining room? Why or why not?

## Tutor Answer

The solutions are ready. Please ask if something is unclear.

1.

a. One uses 2 tbsp = 1 oz of drink mix to obtain 8 oz of iced tea. Thus the ratio of drink mix to iced tea

is 𝟏: 𝟖.

b. To make 32 oz of iced tea we should use such quantity 𝑥 of drink mix that

𝑥: 32 = 1: 8.

By the property of a proportion 𝑥 =

32∙1

8

= 𝟒 (𝑜𝑧).

c. From b. we know that we should use 4 oz for this. And because 1 oz = 2 tbsp we see that 4 oz is 2

times more tbsps, i.e. 4 ∙ 2 = 𝟖 (𝑡𝑏𝑠𝑝).

2. 𝑅(−4, −3), 𝑆(0,5), 𝑇(7, −3).

a.

b. The sides’ lengths are

𝑅𝑆 = √(−4 − 0)2 + (−3 − 5)2 = √16 + 64 = √80 = 4√5,

2

𝑆𝑇 = √(0 − 7)2 + (5 − (−3)) = √49 + 64 = √113,

2

2

𝑇𝑅 = √(7 − (−4)) + (−3 − (−3)) = √112 = 11.

Thus the perimeter is 𝟒√𝟓 + √𝟏𝟏𝟑 + 𝟏𝟏.

c. The base 𝑅...

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