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Triangles

Short Answer Type

281. Two poles of heights 6 metres and 11 metres stand on a plane ground. If the distance between their feet is 12 metres, find the distance between their tops.

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282. A ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall and its top reaches a window 6 m above the ground. Find the length of the ladder.

Solution not provided.
Ans. 6.5 m.

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283. A ladder 5 metres long reaches windows (on the opposite sides of a road) which are 4 metres and 3 metres high from the ground. Find the width of the road.

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284. A ladder 13 m long, placed against a wall, reaches a window 12 m above the ground. Due to some, the foot of the ladder slipped 7 m. How high above the ground is the other end of the ladder now?

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285. In the given figure considering triangles BEP and CPD, prove that BP × PD = EP × PC.

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286. A right triangle has hypotenuse of length p cm. If (q - p) = 2. Express the length of third side of the right triangle in terms of q.

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287. In figure, ∠1 = ∠2 and ∠3 = ∠4 show that PT. QR = PR . ST.

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288. In the given figure, ABC is a right-angled triangle, right angled at C. Find the lengths of AE and DE.

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289. E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that ∆ABE ~ ∆CFB.

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Long Answer Type

290. ABCD is a trapezium with AB || DC, E and F are points on non-parallel sides AD and BC respectively such that EF is parallel to AB show that

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