In right triangle RST below, altitude SV is drawn to
1 answer:
Answer:
ST = 12.2
Step-by-step explanation:
See the attached diagram of the triangle.
Here, Δ RST, Δ RSV and Δ STV all are right triangles.
If we assume that, ST = x and SR = y, then
From Δ RSV and Δ STV we get,
SV² = RS² - RV² = ST² - VT²
⇒ y² - 4.2² = x² - 10.3²
⇒ x² - y² = 88.45 .......... (1)
Now, from Δ RST, we have
ST² + SR² = RT²
⇒ x² + y² = (10.3 + 4.2)² = 210.25 .............. (2)
Now, adding equations (1) and (2) we get,
2x² = 298.7
⇒ x² = 149.35
⇒ x = 12.2 (Rounded to the nearest tenth}
So, ST = 12.2 (Answer)
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Answer:
Step-by-step explanation:
First, you gotta work out the hypotenuse of ABC, which is AC.
To do that, you need to figure out the scale factor between the two right-angled triangles. You can do that for this question because this is a similar shapes question.
12.5/5 = 2.5
The scale factor length between the two triangles is 2.5.
You can use 2.5 now to work out AC, so AC would be 13 x 2.5, which gives 32.5.
Now that you've got the hypotenuse and BC of ABC, you can use Pythagoras's theorem to work out the length of AB
Pythagoras's theorem =
a = BC = 12.5
b = AB = we need to work this out
c = AC (the hypotenuse we just worked out) = 32.5
Let's both simplify and rearrange this at the same time so that we have our b on one side.
= 1056.25 - 156.25
b =
b =
b = AB = 30 We've found b or AB, now we can work out the perimeter of ABC.
Perimeter of ABC = AB + BC + AC
= 30 + 12.5 + 32.5
= 75 Here's the perimeter for ABC.