SOLUTION: Find an expression that represents (a) the perimeter and (b) the area of each figure. Give answers in simplified form. (Assume all measures are given in appropriate units. the

Algebra ->  Triangles -> SOLUTION: Find an expression that represents (a) the perimeter and (b) the area of each figure. Give answers in simplified form. (Assume all measures are given in appropriate units. the       Log On


   

Question 1201134: Find an expression that represents (a) the perimeter and (b) the area of each figure. Give answers in simplified form. (Assume all measures are given in appropriate units.
the image is in google drive of the geometry problem (please i really need help)
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https://drive.google.com/file/d/1soMyK85bSwT9CZE00RdpANa9qN3KR3pM/view?usp=sharing
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answers:
(a) perimeter+=+matrix%281%2C2%2C24%2F%28p%5E2%29%2Cunits%29
(b) area+=+matrix%281%2C3%2C24%2F%28p%5E4%29%2Csquare%2Cunits%29

Replace "units" with something more meaningful (eg: centimeters) if your teacher requires it.
p+%3C%3E+0 to avoid a division by zero error.

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Explanation:

Part (a)

The perimeter is the distance around the exterior.
It's the amount of fencing you need to enclose the triangle.

Therefore, we add up the three sides.
Each is a fraction involving p%5E2 in the denominator.
Meaning we'll add the numerators and set that sum over top the denominator p%5E2
Recall that A%2FC+%2B+B%2FC+=+%28A%2BB%29%2FC when adding fractions of the same denominator.

Here's how the steps could look to compute the perimeter.
perimeter+=+side1%2Bside2%2Bside3
perimeter+=+8%2F%28p%5E2%29%2B6%2F%28p%5E2%29%2B10%2F%28p%5E2%29
perimeter+=+%288%2B6%2B10%29%2F%28p%5E2%29
perimeter+=+24%2F%28p%5E2%29 where p+%3C%3E+0

This is another way to format the steps
perimeter = side1+side2+side3
perimeter = 8/(p^2)+6/(p^2)+10/(p^2)
perimeter = (8+6+10)/(p^2)
perimeter = 24/(p^2)

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Part (b)

matrix%281%2C4%2Carea%2Cof%2Ca%2Ctriangle%29+=+%281%2F2%29%2Abase%2Aheight
area+=+%281%2F2%29%2A%286%2F%28p%5E2%29%29%2A%288%2F%28p%5E2%29%29
area+=+%281%2A6%2A8%29%2F%282%2Ap%5E2%2Ap%5E2%29
area+=+48%2F%282%2Ap%5E4%29
area+=+24%2F%28p%5E4%29 where p+%3C%3E+0

Side notes:
  • The base and height of a triangle are ALWAYS perpendicular to one another (i.e. they form a 90 degree angle).
  • The base and height are the legs of the right triangle. We ignore the hypotenuse when computing the area.
  • The order of base and height doesn't matter.
  • For each expression involving the perimeter and area, the value of p cannot be zero. This is to avoid a division by zero error.
  • The 6-8-10 right triangle has the property that both area and perimeter are "24" when ignoring the units vs square units portions. There are other triangles that have this property as discussed in this video