Answer:
I added the picture as an attached file below
Step-by-step explanation:
Hope it helps:)
WILL GIVE BRAINLST HAVE A AMAZING DAy !!
1 answer:
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<h3>Given</h3>
- ΔABC
- A(-3, -1), B(0, 3), C(1, 2)
- the length of the perimeter of ΔABC to the nearest tenth
The perimeter of a triangle is the sum of the lengths of its sides. The length of each side can be found using the Pythagorean theorem. Effectively, each pair of points is treated as the end-points of the hypotenuse of a right triangle with legs parallel to the x- and y-axes. The leg lengths are the differences betweeen the x- and y- coordinates of the points.
The difference of the x-coordinates of segment AB are 0-(-3) = 3. The y-coordinate difference is 3-(-1) = 4. So, the leg lengths of the right triangle whose hypotenuse is segment AB are 3 and 4. The Pythagorean theorem tells us
... AB² = 3² +4² = 9 +16 = 25
... AB = √25 = 5
You may recognize this as the 3-4-5 triangle often introduced as one of the first ones you play with when you learn the Pythagorean theorem.
LIkewise, segment AC has coordinate differences of ...
... C - A = (1, 2) -(-3, -1) = (4, 3)
These are the same leg lengths (in the other order) as for segment AB, so its length is also 5.
Segment BC has coordinate differences ...
... C - B = (1, 2) -(0, 3) = (1, -1)
The length of the line segment is figured as the root of the sum of squares, even though one of the coordinate differences is negative. The leg lengths of the right triangle used for finding the length of BC are the absolute value of these differences, or 1 and 1. Then the length BC is
... BC = √(1² +1²) = √2 ≈ 1.4
So the perimeter of the triangle ABC is
... AB + BC + AC = 5 + 1.4 + 5 = 11.4 . . . . perimeter of ∆ABC in units
_____
Please be aware that the advice to "round each step" is <em>bad advice,</em> in general. For real-world math problems, you only round the final result. You always carry at least enough precision in the numbers to ensure that there will not be any error in the final rounding.
In this problem, the only number that is not an integer is √2, so it doesn't really matter.
Have a look at the image attachment. I've added the points A, B, C, D such that
A = base of the diving board pole, or location of the pool deck
B = the location 1.6 meters directly above point A
C = location of the person's eyes
D = diving board location
The goal is to find the length of segment AD
We are given
AB = 1.6
BC = 3.67
what we want to find is
BD = x
Due to the fact we have similar right triangles ABC and CBD, we can form the proportion below and solve for x
AB/BC = BC/BD
1.6/3.67 = 3.67/x
1.6*x = 3.67*3.67
1.6*x = 13.4689
1.6*x/1.6 = 13.4689/1.6
x = 8.4180625
So BD is 8.4180625 meters
Use this to find the length of AD
AD = AB + BD
AD = 1.6 + 8.4180625
AD = 10.0180625
which rounds to 10.0 meters when rounding to the nearest tenth (one decimal place)
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Answer: choice D) 10.0 m
A = base of the diving board pole, or location of the pool deck
B = the location 1.6 meters directly above point A
C = location of the person's eyes
D = diving board location
The goal is to find the length of segment AD
We are given
AB = 1.6
BC = 3.67
what we want to find is
BD = x
Due to the fact we have similar right triangles ABC and CBD, we can form the proportion below and solve for x
AB/BC = BC/BD
1.6/3.67 = 3.67/x
1.6*x = 3.67*3.67
1.6*x = 13.4689
1.6*x/1.6 = 13.4689/1.6
x = 8.4180625
So BD is 8.4180625 meters
Use this to find the length of AD
AD = AB + BD
AD = 1.6 + 8.4180625
AD = 10.0180625
which rounds to 10.0 meters when rounding to the nearest tenth (one decimal place)
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Answer: choice D) 10.0 m