Answer:
The percent increase in the perimeter is 337.5%
Step-by-step explanation:
The easiest way to approach this problem is by using consecutively the simple rule of three.
If the first triangle has sides of length two then, we can compute the second triangle's sides length as follows:
2 units------100%
X units------150%
this way
.
Now for the third triangle we repeat the same process
3 units------100%
X units------150%
getting that the length of the sides for the third triangle is
.
Now for the last triangle we repeat the same process
4.5 units------100%
X units------150%
getting that the length of the sides for the last triangle is
.
Now, we need to know the perimeter of the first and last triangle. This can be calculated as the sum of the length of the sides of the triangle.
For the first triangle

and for the last triangle
.
To compute the percent increase in the perimeter from the first to the fourth triangle we will use one last simple rule of three (this time the percentage will be the variable)
6 units------100%
20.25 units------X%
so
.
m∠X + m∠Y < 90° is true.
<h3>How to solve it?</h3>
XYZ is a triangle.
We have to find the option that is true about △XYZ.
By angle sum property of a triangle,
The sum of all the interior angles of a triangle is always equal to 180°.
So, ∠X + ∠Y + ∠Z = 180°
Given, m∠Z > m∠X + m∠Y.
This implies that ∠Z is greater than the sum of the angles ∠X and ∠Y.
so, ∠X + ∠Y must be less than 90°.
Hence, we can say that ∠X + ∠Y < 90°
To know more about triangles, visit:
brainly.com/question/1968095
#SPJ4