Question

In the adjoining △ABC, points X, Y and Z are the midpoints of sides AB, BC and AC respectively. If AB = 5, BC = 11 and AC = 9, then the perimeter of △XYZ = ________​

Answer 1

Answer:

Since X , Y , Z are midpoint on sides AB, BC and CA respectively. Then according to Mid point theorem:-

if x is midpoint

$\frac{1}{2} ab = yz \\ \\ \frac{1}{2} \times 5 = 2.5$

y z= 2.5 ------1

if y is midpoint

$\frac{1}{2} bc = xz \\ \\ \frac{1}{2} \times 11 = 5.5$

xz = 5.5 ------2

if z is midpoint

$\frac{1}{2} ca = xy \\ \\ \frac{1}{2} \times 9 = 4.5$

xy = 4.5 ------3

perimeter of Triangle xyz,

xy+yz+xz = 2.5+5.5+4.5

= 12.5 units