Question

Triangle ABE is similar to triangle ACD. Find y.

3.4

2.7

4.5

2.1

Answer 1

y = 4.5.

Explanation:

Triangles ABE and ACD are similar, so their corresponding sides are in the same ratio.

AB/AC = AE / AD

Now AD = y + ED = y + 3, so:

3/5 = y / (y + 3)

5y = 3y + 9

2y = 9

y = 4.5.

Answer 2

Explanation:

∆ ABE is similar to angle ACD. This means that the ratio of the length of each side of ∆ABE to the length of the corresponding side of ∆ ACD is constant. Therefore,

AB/AC = BE/CD = AE/AD

Therefore,

5/3 = (y + 3)/y

Cross multiplying, it becomes

5 × y = 3(y + 3)

5y = 3y + 9

5y - 3y = 9

2y = 9

Dividing the left hand side and the right hand side of the equation by 2, it becomes

2y/2 = 9/2

y = 4.5