Midsegment of a Triangle: Calculating perimeter

Examples with solutions for Midsegment of a Triangle: Calculating perimeter

Exercise #1

Calculate the perimeter of triangle ADE given that DE is the midsegment of triangle ABC.

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Video Solution

Step-by-Step Solution

In order to calculate the perimeter of triangle ADE \triangle ADE we need to find the lengths of its sides,

Let's now refer to the given information that DE DE is a median in ABC \triangle ABC and therefore a median in a triangle equals half the length of the side it does not intersect, additionally we'll remember the definition of a median in a triangle as a line segment that extends from the midpoint of one side to the midpoint of another side, we'll write the property mentioned (a) and the fact derived from the given definition (b+c):

a.

DE=12BC DE=\frac{1}{2}BC b.

AD=12AB AD=\frac{1}{2}AB c.

AE=12AC AE=\frac{1}{2}AC\\ Additionally, the given data in the drawing are:

d.

BC=8 BC=8 e.

AB=6 AB=6 f.

AC=10 AC=10 Therefore, we will substitute d', e', and f' respectively in a', b', and c', and we get:

g.

DE=12BC=128=4 DE=\frac{1}{2}BC=\frac{1}{2}\cdot8=4 h.

AD=12AB=126=3 AD=\frac{1}{2}AB=\frac{1}{2}\cdot6=3 i.

AE=12AC=1210=5 AE=\frac{1}{2}AC=\frac{1}{2}\cdot10=5 888444333333555555AAABBBCCCDDDEEE

Therefore the perimeter of ADE \triangle ADE is:

j.

PADE=DE+AD+AE=4+3+5=12 P_{ADE}=DE+AD+AE=4+3+5=12 Therefore the correct answer is answer d.

Answer

12

Exercise #2

DE is the midsection of triangle ABC.

What is the perimeter of triangle CDE?

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Video Solution

Answer

6

Exercise #3

DE is the midsection of triangle ABC.

What is the perimeter of triangle BDE?

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Video Solution

Answer

18

Exercise #4

Calculate the perimeter of triangle AED given that DE is the midsegment of triangle ABC.

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Video Solution

Answer

23

Exercise #5

Calculate the perimeter of triangle EBD given that DE is the midsegment of triangle ABC.

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Video Solution

Answer

18

Exercise #6

Calculate the perimeter of triangle EBD given that DE is the midsegment of triangle ABC.

181818121212181818AAABBBCCCDDDEEE

Video Solution

Answer

24

Exercise #7

Calculate the perimeter of triangle AED given that DE is the midsegment of triangle ABC.

1010103X+2.53X+2.53X+2.51010102X2X2XAAABBBCCCDDDEEE

Video Solution

Answer

15

Exercise #8

Calculate the perimeter of triangle ADE given that DE is the midsegment of triangle ABC.

1212125X+15X+15X+11010103X3X3XAAABBBCCCEEEDDD

Video Solution

Answer

13

Exercise #9

Calculate the perimeter of triangle ADE given that DE is the midsegment of triangle ABC.

6661010102.5X2.5X2.5XAAABBBCCCEEEDDD4X+2

Video Solution

Answer

13

Exercise #10

Given that DE is the mid-segment in triangle ABC

DF is the mid-segment in triangle ABC

EF is the mid-segment in triangle ABC

What is the perimeter of triangle FDE?

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Video Solution

Answer

22.5