Question

A triangle has sides $35mm,54mm$ and $61mm$ long. What is its area?

• A. $420\sqrt{5}$ $m{m}^2$
• B. $420\sqrt{3}$ $m{m}^2$
• C. $220\sqrt{5}$ $m{m}^2$
• D. None of the above

Answer 1

Answer: (A)

$420\sqrt{5}$ $m{m}^2$

Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}$.
For triangle with sides $35mm,54mm$ and $61mm$, $s=\frac{35+54+61}{2}=75mm$
Area of the triangle $=\sqrt{75(75-35)(75-54)(75-61)}$

$=\sqrt{75\times 40\times 21\times 14}$

$=\sqrt{25\times 3\times 5\times 8\times 7\times 3\times 7\times 2}$

$=5\times 3\times 4\times 7\times \sqrt{5}$

$=420\sqrt{5}{mm}^2$