Question

A, B, and C are pegs on the bank of a canal which has

parallel straight sides. C and D are directly opposite

each other. AB = 30 m and BC = 140 m.

When I walk from A directly away from the bank,

I reach a point E, 25 m from A, such that E, B, and

D line up. How wide is the canal?

Answer 1

116.67 m

Explanation:

Two triangles are said to be similar if their corresponding angles are equal and the ratio of their sides are in the same proportion.

From the image attached:

∠A = ∠C = 90° (right angled triangle).

∠ABE = ∠CBD (vertically opposite angles are equal to each other)

The angle-angle similarity postulate states that If two angles of one triangle are equal to two angles of another triangle, then both triangles must be similar. Hence:

Since, ∠A = ∠C and ∠ABE = ∠CBD, we can say that ΔABE and ΔCBD are similar triangles. Since they are similar, the ratio of their corresponding sides is equal. Therefore:

BC / AB = CD / AE

BC = 140 m, AB = 30 m, AE = 25 m

substituting:

140 / 30 = CD / 25

CD = (140 / 30) * 25

CD = 116.67 m

The width of the canal = CD = 116.67 m