Advertisements
Advertisements
Question
In the adjoining figure,
seg XY || seg AC, If 3AX = 2BX
and XY = 9 then find the length of AC.
Solution
3AX = 2BX
∴`( AX)/(BX) = 2/3`
`therefore(AX+BX)/(BX)=3+2/3` ...................(By componando)
`therefore(AB)/(BX) = 5/3`
In ΔBCA and ΔBYX,
∠B ≅ ∠B
∠BCA ≅ ∠BYX ................. (Corresponding angles)
∴ ΔBCA ∼ ΔBYX ................. (A-A test of similarity)
∴ `(BA)/(BX)=(AC)/(XY)`
∴ `5/3 = (AC)/9`
∴ 3 × AC = 45
∴ AC = 15
APPEARS IN
RELATED QUESTIONS
In the given figure, PS is the bisector of ∠QPR of ΔPQR. Prove that `(QS)/(SR) = (PQ)/(PR)`
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 = 8cm, AB = 12 cm and AE = 12 cm, find CE.
In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC
If AD = 4x − 3, AE = 8x – 7, BD = 3x – 1 and CE = 5x − 3, find the volume of x.
D and E are the points on the sides AB and AC respectively of a ΔABC such that: AD = 8 cm, DB = 12 cm, AE = 6 cm and CE = 9 cm. Prove that BC = 5/2 DE.
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.
In the adjoining figure, ABC is a triangle in which AB = AC. IF D and E are points on AB and AC respectively such that AD = AE, show that the points B, C, E and D are concyclic.
In the given figure, ∠ACB 90° CD ⊥ AB Prove that `(BC^2)/(AC^2)=(BD)/(AD)`
In ΔABC, AB = AC. Side BC is produced to D. Prove that `AD^2−AC^2`= BD.CD
ABC is an isosceles triangle, right-angled at B. Similar triangles ACD and ABE are constructed on sides AC and AB. Find the ratio between the areas of ΔABE and ΔACD.
State and converse of Thale’s theorem.
In triangle BMP and CNR it is given that PB= 5 cm, MP = 6cm BM = 9 cm and NR = 9cm. If ΔBMP∼ ΔCNR then find the perimeter of ΔCNR
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.
In fig, seg DE || sec BC, identify the correct statement.
In fig., line BC || line DE, AB = 2, BD = 3, AC = 4 and CE = x, then find the value of x
From fig., seg PQ || side BC, AP = x + 3, PB = x – 3, AQ = x + 5, QC = x – 2, then complete the activity to find the value of x.
In ΔPQB, PQ || side BC
`"AP"/"PB" = "AQ"/(["______"])` ...[______]
`(x + 3)/(x - 3) = (x + 5)/(["______"])`
(x + 3) [______] = (x + 5)(x – 3)
x2 + x – [______] = x2 + 2x – 15
x = [______]
In ΔABC, AB = 6 cm and DE || BC such that AE = `1/4` AC then the length of AD is ______.
ΔABC ~ ΔDEF. If AB = 4 cm, BC = 3.5 cm, CA = 2.5 cm and DF = 7.5 cm, then the perimeter of ΔDEF is ______.
In figure, PA, QB, RC and SD are all perpendiculars to a line l, AB = 6 cm, BC = 9 cm, CD = 12 cm and SP = 36 cm. Find PQ, QR and RS.
In the given figure, Sand Tare points on sides PQ and PR, respectively of ΔPQR such that ST is parallel to QR and SQ = TR. Prove that ΔPQR is an isosceles triangles.
