Question

Rashil walked around the triangular park and remembered that two of the park's sides were $60\text{m}\&65\text{m}$. He forgot to measure the third side. Finally, he tried to estimate the length of third side. Choose the correct estimation. Let third side be $a$

• A. $5\text{m}<a<125\text{m}$
• B. $125\text{m}<a$
• C. $5\text{m}\le a\le 125\text{m}$
• D. All the above are possible.

Answer 1

The correct option is A $5\text{m}<a<125\text{m}$

It has been given that the park is triangular in shape, and we know that any triangle has the property that any two of its sides' sum should be greater than third side.

Now, in this question we know two sides are $60$ m and $65$ m.

So, the length of third side should be less than the sum of other two sides.

Hence, length of the third side is less than $(65+60)$ m
$\Rightarrow$ Length of third side $<125\text{m}$

Also, $60\text{m}+a>65\text{m}$
$\Rightarrow a>5\text{m}$
Hence $5\text{m}<a<125\text{m}$
So, option$\left(a\right)$ correct.