Advertisements
Advertisements
Question
In Δ PQR, points S and T
are the midpoints of sides PQ
and PR respectively.
If ST = 6.2 then find the length of QR.
Solution
In Δ PQR, S and T are midpoints of side PQ and side PR.
ST = 6.2
ST= `1/2` × QR ...............(Theorem of midpoints of two sides of
a triangle.)
`∴6.2 = 1/2`× QR
∴QR = 6.2 × 2
∴QR = 12.4
APPEARS IN
RELATED QUESTIONS
In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC
If AD = 6 cm, DB = 9 cm and AE = 8 cm, find AC.
In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC
If AD = 8x − 7, DB = 5x − 3, AE = 4x − 3 and EC = (3x − 1), find the value of x.
In three line segments OA, OB, and OC, points L, M, N respectively are so chosen that LM || AB and MN || BC but neither of L, M, N nor of A, B, C are collinear. Show that LN ||AC.
D and E are points on the sides AB and AC respectively of a ΔABC such that DE║BC.
If` (AD)/(AB) = 8/15 and EC = 3.5cm`, find AE.
In the given figure, ABCD is a trapezium in which AB║DC and its diagonals intersect at O. If AO = (5x – 7), OC = (2x + 1) , BO = (7x – 5) and OD = (7x + 1), find the value of x.
ABCD is a parallelogram in which P is the midpoint of DC and Q is a point on AC such that CQ = `1/4` AC. If PQ produced meets BC at R, prove that R is the midpoint of BC.
ΔABC is an isosceles triangle with AB = AC = 13cm. The length of altitude from A on BC is 5cm. Find BC.
ΔABC is am equilateral triangle of side 2a units. Find each of its altitudes.
In a ABC , AD is a median and AL ⊥ BC .
Prove that
(a) `AC^2=AD^2+BC DL+((BC)/2)^2`
(b) `AB^2=AD^2-BC DL+((BC)/2)^2`
(c) `AC^2+AB^2=2.AD^2+1/2BC^2`
State and converse of Thale’s theorem.
In the adjoining figure,
seg XY || seg AC, If 3AX = 2BX
and XY = 9 then find the length of AC.
In fig, seg DE || sec BC, identify the correct statement.
In fig., PS = 2, SQ = 6, QR = 5, PT = x and TR = y. Then find the pair of value of x and y such that ST || side QR.
In ΔABC, AB = 6 cm and DE || BC such that AE = `1/4` AC then the length of AD is ______.
Find the value of x for which DE || AB in figure.
In figure, line segment DF intersect the side AC of a triangle ABC at the point E such that E is the mid-point of CA and ∠AEF = ∠AFE. Prove that `(BD)/(CD) = (BF)/(CE)`.
In the given figure, ABC is a triangle in which DE||BC. If AD = x, DB = x – 2, AE = x + 2 and EC = x – 1, then find the value of x.