Q23 of 32 Page 6

ABC is an isosceles triangle, right-angled at B. Similar triangles ACD and ABE are constructed on sides AC and AB. Find the ratio between the areas of ΔABE and ΔACD.

(CBSE 2002)

ΔABC is right triangle.


Applying Pythagoras theorem we get,


AC2 = AB2 + BC2 {∵ AB = BC}


⇒ AC2 = 2AB2


Given that the two triangles ΔACD and ΔABE are similar.


We know that if two triangles are similar then the ratio of their areas is equal to the ratio of the squares of their corresponding altitudes.


More from this chapter

All 32 →
21

If the areas of two similar triangles are equal, prove that they are congruent. (CBSE 2010)

 22

ΔABC is an isosceles triangle with AB = AC = 13 cm. The length of altitude from A on BC is 5 cm. Find BC.(CBSE 2000)

 24

Two poles of heights 6 m and 11 m stand on aplane ground. If the distance between the feetof the poles is 12 m, find the distance between their tops. (CBSE 2002)

 25

In ΔABC, D is the midpoint of BC and AE ⊥ BC. If AC > AB, show that

AB2 = AD2 — BC • DE + 1/4 BC2 (CBSE 2006)