Advertisements
Advertisements
प्रश्न
Walls of two buildings on either side of a street are parallel to each other. A ladder 5.8 m long is placed on the street such that its top just reaches the window of a building at the height of 4 m. On turning the ladder over to the other side of the street, its top touches the window of the other building at a height 4.2 m. Find the width of the street.
Advertisements
उत्तर
Let the length of the ladder be 5.8 m.
According to Pythagoras theorem,
In ΔEAB,
EA2 + AB2 = EB2
∴ (4.2)2 + AB2 = (5.8)2
∴ 17.64 + AB2 = 33.64
∴ AB2 = 33.64 − 17.64
∴ AB2 = 16
∴ AB = 4 m
In ∆DCB,
DC2 + CB2 = DB2
∴ (4)2 + CB2 = (5.8)2
∴ 16 + CB2 = 33.64
∴ CB2 = 33.64 − 16
∴ CB2 = 17.64
∴ CB = 4.2 m
From (1) and (2), we get
AB + BC = 4 + 4.2 = 8.2 m
∴ the width of the street is 8.2 m.
संबंधित प्रश्न
The diagonal of a rectangular field is 16 metres more than the shorter side. If the longer side is 14 metres more than the shorter side, then find the lengths of the sides of the field.
A man goes 10 m due east and then 24 m due north. Find the distance from the starting point
In a right triangle ABC right-angled at C, P and Q are the points on the sides CA and CB respectively, which divide these sides in the ratio 2 : 1. Prove that
`(i) 9 AQ^2 = 9 AC^2 + 4 BC^2`
`(ii) 9 BP^2 = 9 BC^2 + 4 AC^2`
`(iii) 9 (AQ^2 + BP^2 ) = 13 AB^2`
Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, ho much string does she have out (see Figure)? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?
Which of the following can be the sides of a right triangle?
2.5 cm, 6.5 cm, 6 cm
In the case of right-angled triangles, identify the right angles.
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(A)\[7 + \sqrt{5}\]
(B) 5
(C) 10
(D) 12
The given figure shows a quadrilateral ABCD in which AD = 13 cm, DC = 12 cm, BC = 3 cm and ∠ABD = ∠BCD = 90o. Calculate the length of AB.
In triangle ABC, AB = AC and BD is perpendicular to AC.
Prove that: BD2 − CD2 = 2CD × AD
In triangle ABC, angle A = 90o, CA = AB and D is the point on AB produced.
Prove that DC2 - BD2 = 2AB.AD.
Find the side of the square whose diagonal is `16sqrt(2)` cm.
In the figure below, find the value of 'x'.
In the right-angled ∆PQR, ∠ P = 90°. If l(PQ) = 24 cm and l(PR) = 10 cm, find the length of seg QR.
The length of the diagonals of rhombus are 24cm and 10cm. Find each side of the rhombus.
In an equilateral triangle ABC, the side BC is trisected at D. Prove that 9 AD2 = 7 AB2.
A point OI in the interior of a rectangle ABCD is joined with each of the vertices A, B, C and D. Prove that OB2 + OD2 = OC2 + OA2
AD is perpendicular to the side BC of an equilateral ΔABC. Prove that 4AD2 = 3AB2.
∆ABC is right-angled at C. If AC = 5 cm and BC = 12 cm. find the length of AB.
In triangle ABC, line I, is a perpendicular bisector of BC.
If BC = 12 cm, SM = 8 cm, find CS
In figure, PQR is a right triangle right angled at Q and QS ⊥ PR. If PQ = 6 cm and PS = 4 cm, find QS, RS and QR.
In ∆PQR, PD ⊥ QR such that D lies on QR. If PQ = a, PR = b, QD = c and DR = d, prove that (a + b)(a – b) = (c + d)(c – d).
