Question

If AC = 7 m and CE = 25 m, find the breadth of the river.
A. 18 metres
B. 20 metres
C. 22 metres
D. 24 metres.

Answer 1

Answer:

Width of river = 24 cm

Step-by-step explanation:

AC = CD

B , C , E are in same line

Compare Δ ACB  &  Δ DCE

AC = CD

∠ACB = ∠DCE  ( vertically opposite angle)

∠CAB = ∠CDE = 90°

=> Δ ACB  ≅  Δ DCE

=> DE = AB = ( width of river)

* CE = BC

CE = 25 cm => BC = 25 cm

AC = 7 cm =

AB² = AC² - BC²

=> AB² = 25² - 7²

=> AB² = (25 + 7)(25 - 7)

=> AB² = 32 * 18

=> AB² = 4² * 2 * 3² * 2

=> AB² = 4² * 3² * 2²

=> AB = 4 * 3 * 2

=> AB = 24 cm

Width of river = 24 cm

Answer 2

given CE = 25 m

AC = 7m (length)

using Pythagoras theorem,

$\\ \\ \\ \\ {(CE)}^{2} = ( {AC})^{2} + ( { AE})^{2} \\ \\ \\ \sqrt{( {25)}^{2} - ( {7)}^{2} } = A E \\ \\ \\ \\ AE = 24m \: - - - option \: d \:$