Question

Question 4
Write True or False and give reasons for your answer:

A $\Delta ABC$ can be constructed in which BC = 6cm, $\angle C={30}^{\circ }$ and AC – AB = 4cm.

Answer 1

True

We know that a triangle can be constructed if the sum of its two sides is greater than the third side.

i.e., in $\Delta ABC$, AB + BC > AC

i.e., in $\Delta ABC$,
$\Rightarrow$ BC > AC - AB

$\Rightarrow$ 6>4, which is true, so $\Delta ABC$ with given conditions can be constructed.