Question

In ABC, X is the midpoint of AB. Y is the midpoint of BC and Z is the midpoint of AC If BC = 14 m, YZ = 3 m, and XY = 7 m, what is the perimeter of ABC? Perimeter = m​

Answer 1

The calculated value of the perimeter of triangle ABC is 34 meters

How to determine the perimeter of triangle ABC

From the question, we have the following parameters that can be used in our computation:

• X is the midpoint of AB.
• Y is the midpoint of BC and
• Z is the midpoint of AC

Also, we have

BC = 14 m, YZ = 3 m, and XY = 7 m,

This means that

The perimeter of triangle ABC is twice the perimeter of triangle XYZ

The perimeter of a triangle is the sum of the side lengths)

So, we have

Perimeter = 14 + 2 * (3 + 7)

Evaluate

Perimeter = 34

Hence, the perimeter of triangle ABC is 34 meters

Answer 2

The perimeter of the triangle is 26 m.

How to calculate the perimeter of a triangle.

Midpoint Theorem states that in a triangle, the line segment joining the midpoints of two sides is parallel to the third side and half its length.

Given,

X is midpoint of AB

Y is midpoint of BC

Z is midpoint of AC

BC = 14 m

YZ = 3 m

XY = 7 m

Fr

YZ = 1/2* AB(midpoint theorem)

3 = 1/2 AB

AB = 2*3 = 6 m

AXYZ is a parallelogram

If XY = AZ = 7 cm

AX = YZ(opposite side congruent of ||gm)

AX = YZ = 3

AX = 1/2BC(midpoint theorem)

3 = 1/2BC

BC = 3*2

= 6 m

Perimeter of a triangle = Sum of the sides

P = AB + BC + AC

= 6 + 6 + 14

= 26 m

Therefore, perimeter of the triangle is 26 m