Question

Allel...

10. If the midpoints of the sides of AEFG shown below were connected with line segments, what would be the
perimeter of the resulting triangle? Explain how you arrived at your answer.
allel...
E
arall...
of a T...
170 mm
83 mm
110 mm

Answer 1

Perimeter of triangle PQR = 181.5 mm

Explanation:

Midsegment theorem states that,

"Midsegment connecting the midpoints of the two sides of a triangle is parallel and half of the length of the third side"

From the figure attached,

PQ =
`(1)/(2)(EF)`

=
`(83)/(2)`

= 41.5 mm

PR =
`(1)/(2)(GF)`

=
`(110)/(2)`

= 55 mm

QR =
`(1)/(2)(GE)`

=
`(170)/(2)`

= 85 mm

Perimeter of triangle PQR = PQ + QR + PR

= 41.5 + 55 + 85

= 181.5 mm