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lions [1.4K]
3 years ago
6

GEOMETRY HELP!

Mathematics
1 answer:
tigry1 [53]3 years ago
5 0

Answer:

1. Length of BC = 35

2. SU = 3.5

3. AC = 50 inches

4.

<u>Part 1:</u> AB = 10 cm

<u>Part 2:</u> AD = 2 cm

5. Width of River AB = 145.45 ft

Step-by-step explanation:

1.

The length of BC is (x+4)+(2x+1) = 3x+5

Now, if we figure out x, we can plug that in and find length of BC.

Using similarity with the two triangles shown, we can set-up the ratio as:

\frac{8}{12}=\frac{x+4}{2x+1}

<em />

<em>Now, cross multiplying and solving for x:</em>

\frac{8}{12}=\frac{x+4}{2x+1}\\8(2x+1)=12(x+4)\\16x+8=12x+48\\4x=40\\x=\frac{40}{4}=10

Now plugging in x=10 into 3x+5, we have  3(10)+5 = 35

Length of BC = 35

2.

Using pythagorean theorem in triangle PQT, we can solve for QT.

(\sqrt{2})^2+(\sqrt{2})^2=QT^2\\2+2=QT^2\\4=QT^2\\QT=\sqrt{4}=2

QT = RS = 2

Now using pythagorean theorem on Triangle RSU, we can solve for SU. So:

RS^2+SU^2=RU^2\\2^2+SU^2=4^2\\SU^2=4^2-2^2\\SU^2=12\\SU=\sqrt{12}=3.5

SU = 3.5

3.

If we draw a straight line as Segment AC, we have a right triangle with both legs measuring 30 and 40 inches, respectively. AC is the hypotenuse. Using pythagorean theorem, we can find out AC:

AB^2+BC^2=AC^2\\30^2+40^2=AC^2\\2500=AC^2\\AC=\sqrt{2500}=50

Thus AC = 50 inches

4.

<u>AB:</u>

<u />

We can set-up a similarity ratio to solve for AB. We can write:

\frac{12}{20}=\frac{6}{AB}

<em>Now, cross multiplying, we can solve for AB:</em>

\frac{12}{20}=\frac{6}{AB}\\12AB=6*20\\12AB=120\\AB=\frac{120}{12}=10

Thus, AB = 10 cm

<u>AD:</u>

<u />

We know, AB = BF + FD + DA

We also know, FD = 6, AB = 10 and BF & DA are same. So we can write DA in place of BF and solve. Thus:

AB = BF + FD + DA\\10=AD+6+AD\\10-6=2AD\\4=2AD\\AD=2

Thus, AD = 2 cm

5.

A single piece of information is missing from this problem. They have given DE = 32 ft.

Now, we see that triangle EDC is similar to triangle ABC, so their corresponding sides are proportional. Thus we can set-up a ratio as:

\frac{DC}{BC}=\frac{DE}{BA}

Now we can put the information we know and solve for AB, the width of the river.

\frac{DC}{BC}=\frac{DE}{BA}\\\frac{22}{100}=\frac{32}{AB}\\22AB=32*100\\22AB=3200\\AB=\frac{3200}{22}=145.45

Width of River AB = 145.45 ft

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