Q7 of 42 Page 210

A flag pole 4 m tall casts a 6 m., shadow. At the same time, a nearby building casts a shadow of 24m. How tall is the building?

Given, a flag pole 4m tall with shadow 6m


And a building shadow 24m


Need to calculate the building


In Δ ABC and Δ PQR



⇒ ∠ B = ∠ Q = 90°


⇒ ∠ C = ∠ R


At any instance all sun rays are parallel, AC || PR


⇒ by AAA similarity we have in two triangles if the angles are equal, then sides opposite to the equal angles are in the same ratio (or proportional) and hence the triangles are similar.


⇒ Δ ABC ∼ Δ PQR


⇒ By Converse proportionality theorem we have


if a line divides any two sides of a triangle in the same ratio then the line must be parallel to the third side.


⇒


⇒


⇒ PQ =


= 16m


Hence the height of a building is 16m


More from this chapter

All 42 →
5

Diagonals AC and BD of a trapezium ABCD with AB||DC intersect each other at the point ‘O’. Using the criterion of similarity for two triangles, show that

6

AB, CD, PQ are perpendicular to BD. AB = x, CD = y and PQ = z prove that

8

CD and GH are respectively the bisectors of ∠ACE and ∠EGF such that D and H lie on sides AB and FE of Δ ABC and Δ FEG respectively. If Δ ABC ∼ Δ FEG then show that

i.


ii. Δ DCB ∼ ΔHGE


iii. Δ DCA ∼ ΔHGF

 9

AX and DY are altitudes of two similar Δ ABC and ΔDEF. Prove that AX : DY = AB : DE.