Question

Find the area of a triangle whose sides are $12cm,35cm,37cm$.

• A. $210c{m}^2$
• B. $220c{m}^2$
• C. $200c{m}^2$
• D. $208c{m}^2$

Answer 1

Answer: (A)

$210c{m}^2$

Given: $12cm,35cm,37cm$ are the sides of the triangle.

Now,

$\Rightarrow {12}^2+{35}^2=144+1225=1369$

$\Rightarrow {37}^2=1367$

Since, ${12}^2+{35}^2={37}^2$, therefore, the sides are the sides of right angled triangle as they satisfy the Pythagoras Theorem.

Thus, hypotenuse of the triangle is $37cm$ where as the other sides form the base and height of the triangle.

Hence, the area of the triangle $=\frac{1}{2}\times \text{Base}\times \text{Height}$

$=\frac{1}{2}\times 12\times 35$

$=210c{m}^2$.