Question

Measurements of sides of some triangles are given.
Which of the following triangle(s) can be formed with the given measurements ?

• A. $△ABC$ in which $AB=4\text{cm},BC=5\text{cm}\&AC=0.5\text{cm}$
• B. $△ABC$ in which $AB=10\text{cm},BC=5\text{cm}\&AC=7\text{cm}$
• C. $△ABC$ in which $AB=4\text{cm},BC=4\text{cm}\&AC=5\text{cm}$
• D. $△ABC$ in which $AB=10\text{cm},BC=4\text{cm}\&AC=4\text{cm}$

Answer 1

Answer: (B), (C)

$△ABC$ in which $AB=4\text{cm},BC=4\text{cm}\&AC=5\text{cm}$

To construct triangle, the main criteria is that the sum of two sides must be greater than the third side.

In option$\left(a\right)$, $AB+AC=4+0.5=4.5$cm
and $BC=5$cm so $AB+AC<BC$

In option$\left(b\right)$ and $\left(c\right)$,
sum of any two sides is greater than third side.

And, in option$\left(d\right)$,
$AC+BC=4+4$
$AC+BC=8$cm
and $AB=10$cm
here, $AC+BC<AB$
Hence, this triangle is also not possible.
So, option$\left(b\right)$, $\left(c\right)$ are correct.