Advertisements
Advertisements
प्रश्न
In ΔABC, DE || AB. If AB = a, DE = x, BE = b and EC = c. Then x expressed in terms of a, b and c is ______.
विकल्प
`("ac")/"b"`
`("ac")/("b" + "c")`
`("ab")/"c"`
`("ab")/("b" + "c")`
उत्तर
In ΔABC, DE || AB. If AB = a, DE = x, BE = b and EC = c. Then x expressed in terms of a, b and c is `underlinebb((ac)/(b + c))`
Explanation:
In ΔCDE and ΔCAB
∠C = ∠C ...[Common]
∠1 = ∠2 ...[Corresponding angles as DE || AB]
ΔCDE ∼ ΔCAB ...[By AA rule]
`("DE")/("AB") = ("CE")/("BC")` ...[Sides of similar triangles]
`x/"a" = "c"/("b" + "c")`
x = `("ac")/("b" + "c")`
APPEARS IN
संबंधित प्रश्न
In the following figure, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, prove that ΔABD ∼ ΔECF.
In the given figure, D is a point on hypotenuse AC of ΔABC, DM ⊥ BC and DN ⊥ AB, Prove that:
(i) DM2 = DN.MC
(ii) DN2 = DM.AN
ABCD is a parallelogram and APQ is a straight line meeting BC at P and DC produced at Q. Prove that the rectangle obtained by BP and DQ is equal to the AB and BC.
The sides of certain triangles are given below. Determine which of them right triangles are.
9cm, 16cm, 18cm
State the two properties which are necessary for given two triangles to be similar.
In the given figure, ∠AMN = ∠MBC = 76° . If p, q and r are the lengths of AM, MB and BC respectively then express the length of MN of terms of P, q and r.
A 15 metres high tower casts a shadow 24 metres long at a certain time and at the same time, a telephone pole casts a shadow 16 metres long. Find the height of the telephone pole.
A street light bulb is fixed on a pole 6 m above the level of the street. If a woman of height 1.5 m casts a shadow of 3 m, find how far she is away from the base of the pole.
In the given figure, DE ∥ BC, AE = a units, EC = b units, DE = x units and BC = y units. Which of the following is true?
ABCD is a trapezium with AD ∥ BC and AD = 4 cm. If the diagonals AC and BD intersect each other at O such that AO/OC = DO/OB = 1/2, then BC = ______.
