What is the perimeter of the triangle below? Round to the nearest hundredth.
1 answer:
You're going to need to use Pythagoras' theorem to work this one out!
As you know, the perimeter of a triangle is just all the lengths of the sides added up.
We'll start with side AC first. We can see that A is (-8, -4) and C is (-6, -2). That means to get from A to C, we need to go 2 units to the right, and 2 units up. Which means we have our two sides to work out the length from Pythagoras' theorem. 2² + 2² = c², c = √8.
Now we'll move onto side AB. We already know A is (-8, -4) from above, and B is (-7, -8). That means to get from A to B, we have to go 4 units down, and 1 unit to the right. So once again: 4² + 1² = c², c = √17.
Lastly, we'll work out side BC. We know that B is (-7, -8) and C is (-6, -2). That means to get to C from B, we have to go 1 unit to the right and 6 units up. So, again: 1² + 6² = c², c = √37.
Now that we have all of our lengths, we simply just add them up!
√8 + √17 + √37 ≈ 13.03 units.
(I've also attached something to help you visualise how I worked it out.)
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Answer:
BC = 24
Step-by-step explanation:
In the picture attached, the missing triangles are shown:
<u>Data</u>
- AB = 10
- BD = 5
- DE= 12
- Then, AD = 10-5 = 5
As a consequence of the "Side Splitter" Theorem:
AD/DE = AB/BC
Replacing with data and solving for BC
5/12 = 10/BC
BC = 10*12/5 = 24
