Advertisements
Advertisements
प्रश्न
A ladder 15m long reaches a window which is 9m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to other side of the street to reach a window 12m high. Find the width of the street.
Advertisements
उत्तर
let O be the foot of the ladder. Let AO be the position of the ladder when it touches the window at A which is 9m high and CO be the position of the ladder when it touches the window at C which is 12m high.
Using Pythagoras theorem,
In ΔAOB,
BO2 = AO2 - AB2
BO2 = (15m)2 - (9m)2
BO2 = 225m2 - 81m2
BO2 = 144m2
BO2 = (12m)2
BO2 = 12m
Using Pythagoras theorem in ΔCOB,
DO2 = CO2 - CD2
DO2 = (15m)2 - (12m)2
DO2 = 225m2 - 144m2
DO2 = 81m2
DO = 9m
Width of the street
= DO + BO
= 9m + 12m
= 21m.
APPEARS IN
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.
Two towers of heights 10 m and 30 m stand on a plane ground. If the distance between their feet is 15 m, find the distance between their tops
From a point O in the interior of a ∆ABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove
that :
`(i) AF^2 + BD^2 + CE^2 = OA^2 + OB^2 + OC^2 – OD^2 – OE^2 – OF^2`
`(ii) AF^2 + BD^2 + CE^2 = AE^2 + CD^2 + BF^2`
The perpendicular AD on the base BC of a ∆ABC intersects BC at D so that DB = 3 CD. Prove that `2"AB"^2 = 2"AC"^2 + "BC"^2`
PQR is a triangle right angled at P. If PQ = 10 cm and PR = 24 cm, find QR.
Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.
Identify, with reason, if the following is a Pythagorean triplet.
(4, 9, 12)
In the figure: ∠PSQ = 90o, PQ = 10 cm, QS = 6 cm and RQ = 9 cm. Calculate the length of PR.
In the figure, given below, AD ⊥ BC.
Prove that: c2 = a2 + b2 - 2ax.
ABC is a triangle, right-angled at B. M is a point on BC.
Prove that: AM2 + BC2 = AC2 + BM2
In the following figure, OP, OQ, and OR are drawn perpendiculars to the sides BC, CA and AB respectively of triangle ABC.
Prove that: AR2 + BP2 + CQ2 = AQ2 + CP2 + BR2
In triangle PQR, angle Q = 90°, find: PQ, if PR = 34 cm and QR = 30 cm
Find the Pythagorean triplet from among the following set of numbers.
2, 6, 7
Two poles of height 9m and 14m stand on a plane ground. If the distance between their 12m, find the distance between their tops.
From a point O in the interior of aΔABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove that: AF2 + BD2 + CE2 = OA2 + OB2 + OC2 - OD2 - OE2 - OF2
In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.
Prove that : 9(AQ2 + BP2) = 13AB2
The hypotenuse of a right angled triangle of sides 12 cm and 16 cm is __________
In the given figure, ∠T and ∠B are right angles. If the length of AT, BC and AS (in centimeters) are 15, 16, and 17 respectively, then the length of TC (in centimeters) is ______.
For going to a city B from city A, there is a route via city C such that AC ⊥ CB, AC = 2x km and CB = 2(x + 7) km. It is proposed to construct a 26 km highway which directly connects the two cities A and B. Find how much distance will be saved in reaching city B from city A after the construction of the highway.
Two rectangles are congruent, if they have same ______ and ______.
