Question

Construct ΔABC, in which BC=5.2 cm, ∠ACB=45° and perimeter of ΔABC is 10 cm

Answer 1

Answer:

It is impossible.

Step-by-step explanation:

Since we know that

Perimeter of triangle = sum of all sides = AB + BC + CA

And

we are given that

Perimeter = 10 cm  and BC = 5.2 cm

So

10 = AB + 5.2 + CA

And

AB + CA = 10 - 5.2 = 4.8 cm

We have to make the at vertex C = 45°

We know that

Sum of all angles of triangle = 180°

So

∠A + ∠B + ∠C = 180°

∠A + ∠B + 45 = 180°

∠A + ∠B + = 180° - 45° = 135°

The above illustration show that the construction of such a triangle is impossible

Because if we consider the angles in such a way that

∠C = ∠B = 0°

Then the minimum perimeter of triangle is = 5.2 + 5.2 = 10.4 cm

And if we make the angle C greater then zero and the perimeter always greater then 10.4

So

It impossible to construct such a triangle in which BC = 5.2 and ∠C = 45°

And perimeter is 10 cm

See the minimum case of perimeter in the figure show below.