In a ABC, B = 90°, AB = 5 cm. Construction of ABC is not possible if BC - AC = ______________.

△ABC, where \angle B = $$90^\circ$$​​

AB = 5 cm

BC - AC = k

For the triangle to be constructible:

The sum of any two sides must be greater than the third side (triangle inequality).

Pythagoras' theorem:

AC = $$\sqrt{AB^2 + BC^2}$$​​

Let BC - AC = k

Identifying when the given k = BC - AC violates the triangle inequality.

Triangle inequality condition:
For the triangle to exist:

BC + AB > AC and AC + AB > BC

Now, BC = AC + k.

Substituting into the inequality AC + AB > BC:

AC + AB > AC + k

AB > k

Since AB = 5 cm

K < 5 cm

If k ≥ 5 cm, the triangle cannot exist.

Now, Verifying with Options

Option A: k = 2.5 cm
k < 5: Construction is possible.

Option B: k = 4.8 cm

k < 5: Construction is possible.

Option C: k = 6.5 cm

k >5: Construction is not possible.

Option D: k = 4 cm

k < 5: Construction is possible.

Thus, the construction of △ABC is not possible if BC−AC=6.5 cm (Option C).