Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
In Fig. below, M, N and P are the mid-points of AB, AC and BC respectively. If MN = 3 cm, NP = 3.5 cm and MP = 2.5 cm, calculate BC, AB and AC.
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.
The following figure shows a trapezium ABCD in which AB // DC. P is the mid-point of AD and PR // AB. Prove that:
PR = `[1]/[2]` ( AB + CD)
In the figure, give below, 2AD = AB, P is mid-point of AB, Q is mid-point of DR and PR // BS. Prove that:
(i) AQ // BS
(ii) DS = 3 Rs.
In the given figure, AD and CE are medians and DF // CE.
Prove that: FB = `1/4` AB.
In triangle ABC, D and E are points on side AB such that AD = DE = EB. Through D and E, lines are drawn parallel to BC which meet side AC at points F and G respectively. Through F and G, lines are drawn parallel to AB which meets side BC at points M and N respectively. Prove that: BM = MN = NC.
ΔABC is an isosceles triangle with AB = AC. D, E and F are the mid-points of BC, AB and AC respectively. Prove that the line segment AD is perpendicular to EF and is bisected by it.
In ΔABC, D and E are the midpoints of the sides AB and AC respectively. F is any point on the side BC. If DE intersects AF at P show that DP = PE.
In the given figure, PS = 3RS. M is the midpoint of QR. If TR || MN || QP, then prove that:
ST = `(1)/(3)"LS"`
In ∆ABC, AB = 5 cm, BC = 8 cm and CA = 7 cm. If D and E are respectively the mid-points of AB and BC, determine the length of DE.
