in the diagram below of triangle abc, de is a midsegment of triangle abc, de=7, ab=10, and bc=13.find the perimeter
Well, we don't have a diagram, but that won't stop us in this case. A midsegment of a triangle is parallel to one of the sides, and half its length.
Since de=7 is not half of ab=10, nor of bd=13, then that means that it must be half of ac. So, ac=14, and the perimeter is
p = 10 + 13 + 14 = 37
Perimeter is the total of all triangle,so we have a triangle with side 10,13and 14(half of DE ).Now we just have to add this side 10+13+14=37
37 is the perimeter of a triangle
joel
To find the perimeter of triangle ABC, we need to determine the lengths of all three sides: AB, BC, and AC.
In the given diagram, DE is a midsegment of triangle ABC. A midsegment of a triangle connects the midpoints of two sides of the triangle. In this case, DE connects the midpoints of AB and BC.
We are given that DE = 7. Since DE is a midsegment, it is parallel to and half the length of BC. Therefore, BC = 2 * DE = 2 * 7 = 14.
Now, we know that AB = 10 and BC = 14. To find the remaining side AC, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Since AB = 10 and BC = 14, we can see that AB + BC = 10 + 14 = 24, which is greater than AC. Therefore, AC must be greater than the difference between the sum of the two known sides and the unknown side: AC > |AB - BC| = |10 - 14| = 4.
Since AC is constrained between 4 and 24, there could be two possible values for AC. However, given the given diagram and the information provided, we can conclude that AC must be the longer side and therefore, AC = 24.
Now we have the lengths of all three sides: AB = 10, BC = 14, and AC = 24. To find the perimeter, we simply add these three sides together: Perimeter = AB + BC + AC = 10 + 14 + 24 = 48.
Therefore, the perimeter of triangle ABC is 48 units.