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:
<em />
<em>Now, cross multiplying and solving for x:</em>
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.
QT = RS = 2
Now using pythagorean theorem on Triangle RSU, we can solve for SU. So:
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:
Thus AC = 50 inches
4.
<u>AB:</u>
<u />
We can set-up a similarity ratio to solve for AB. We can write:
<em>Now, cross multiplying, we can solve for AB:</em>
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:
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:
Now we can put the information we know and solve for AB, the width of the river.
Width of River AB = 145.45 ft