Advertisements
Advertisements
Question
In a triangle, P, Q and R are the mid-points of sides BC, CA and AB respectively. If AC =
21 cm, BC = 29 cm and AB = 30 cm, find the perimeter of the quadrilateral ARPQ.
Advertisements
Solution
In ΔABC
R and P are the midpoint of AB and BC
∴RP || AC, RP = `1/2` AC [By midpoint theorem]
In a quadrilateral
[A pair of side is parallel and equal]
RP || AQ, RP = AQ
∴RPQA is a parallelogram
AR = `1/2` AB = `1/2 ` × 30 = 15cm
AR = QP = 15 [ ∵ Opposite sides are equal]
⇒ RP = `1/2` AC = `1/2` × 21 = 10 .5cm [ ∵ Opposite sides are equal]
Now,
Perimeter of ARPQ = AR + QP + RP + AQ
= 15 +15 +10.5 +10.5
= 51cm
APPEARS IN
RELATED QUESTIONS
BM and CN are perpendiculars to a line passing through the vertex A of a triangle ABC. If
L is the mid-point of BC, prove that LM = LN.
Prove that the figure obtained by joining the mid-points of the adjacent sides of a rectangle is a rhombus.
ABCD is a quadrilateral in which AD = BC. E, F, G and H are the mid-points of AB, BD, CD and Ac respectively. Prove that EFGH is a rhombus.
In Δ ABC, AD is the median and DE is parallel to BA, where E is a point in AC. Prove that BE is also a median.
In triangle ABC ; D and E are mid-points of the sides AB and AC respectively. Through E, a straight line is drawn parallel to AB to meet BC at F.
Prove that BDEF is a parallelogram. If AB = 16 cm, AC = 12 cm and BC = 18 cm,
find the perimeter of the parallelogram BDEF.
In ΔABC, P is the mid-point of BC. A line through P and parallel to CA meets AB at point Q, and a line through Q and parallel to BC meets median AP at point R. Prove that: AP = 2AR
E is the mid-point of the side AD of the trapezium ABCD with AB || DC. A line through E drawn parallel to AB intersect BC at F. Show that F is the mid-point of BC. [Hint: Join AC]
E is the mid-point of a median AD of ∆ABC and BE is produced to meet AC at F. Show that AF = `1/3` AC.
E and F are respectively the mid-points of the non-parallel sides AD and BC of a trapezium ABCD. Prove that EF || AB and EF = `1/2` (AB + CD).
[Hint: Join BE and produce it to meet CD produced at G.]
D, E and F are respectively the mid-points of the sides AB, BC and CA of a triangle ABC. Prove that by joining these mid-points D, E and F, the triangles ABC is divided into four congruent triangles.
