Question

GEOMETRY HELP!

Answer 1

Answer:

1. Length of BC = 35

2. SU = 3.5

3. AC = 50 inches

4.

Part 1: AB = 10 cm

Part 2: 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:

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

Now, cross multiplying and solving for x:

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

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.

AB:

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

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

Now, cross multiplying, we can solve for AB:

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

Thus, AB = 10 cm

AD:

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