ACT Math : How to find the perimeter of a 45/45/90 right isosceles triangle
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Example Question #9 :45/45/90 Right Isosceles Triangles
What is the perimeter of an isosceles right triangle with an hypotenuse of length
Your right triangle is a
Now, you know that you also have a reference triangle for
This means that you can set up a ratio to find
Your triangle thus could be drawn like this:
Now, notice that you can rationalize the denominator of
Thus, the perimeter of your figure is:
例子问题# 10:45/45/90 Right Isosceles Triangles
What is the perimeter of an isosceles right triangle with an area of
Recall that an isosceles right triangle is also a
or
Now, you know that the area of a triangle is:
For this triangle, though, the base and height are the same. So it is:
Now, we have to be careful, given that our area contains
Thus,
Therefore, your perimeter is:
Example Question #201 :Geometry
A tree is
This is a right triangle where the rope is the hypotenuse. One leg is the radius of the circle, 5 feet. The other leg is half of the tree's height, 12 feet. We can now use the Pythagorean Theorem
Example Question #202 :Geometry
An isosceles right triangle has a hypotenuse of length
The ratio of sides to hypotenuse of an isosceles right triangle is always
Since the perimeter has two of these legs, we just need to multiply this by
So, our perimeter in terms of
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