Question

In ∆ABC, C = 90°. AC :BC = 1:4. Point E is on BC such that BE : CE = 2:3. If AB = 35√17 , find AE.

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Answer 1

AC:BC is given to us as 1:4

Let us take AC as x, so obviously BC is 4x

Le us apply Pythagoras theorem in triangle ABC

AC² + BC² = AB²

Substituting values, we get

x² + (4x)² = (35√17)²

x² + 16x² = (35)²×(√17)²

17x² = (35)²×17

x² = 35²

x = 35

So AC is 35 units whereas BC is 140 units.

Now consider the side BC

We have BE:CE = 2:3

Let us assume BE as 2y, so CE will be 3y

But we know that CE+BE = BC

Substituting values, we get

3y+2y = 140

5y = 140

y = 28

So the length of CE is 3y = 84 units.

Now let us consider the triangle ACE.

Let us apply pythagoras theorem.

AC² + CE² = AE²

AE² = 35² + 84²

AE² = 7²×(5²+12²)

AE² = 7²×169

AE² = 7²×13²

AE = 7×13

AE = 91 units.

SO THE ANSWER IS 91 UNITS.