Question

Fred, a carpenter, is making a triangular wooden base to support a tripod stand. When the tripod is upright, the straight line distances between the legs at the base of the tripod are $30\text{cm},40\text{cm, and}50\text{cm}$. Construct and find the area of the triangular wooden base.
(Note: Assume that the thickness of the triangular wooden base is negligible.)

• A. $5m^2$
• B. $20m^2$
• C. $6m^2$
• D. $50c{m}^2$

Answer 1

The correct option is C $6m^2$

Since all the three sides of the triangular wooden piece are given, we can construct the triangle using the SSS criterion.

1. First, draw a line $AB$ of length $40\text{cm}$.


2. Next, cut an arc of radius $30\text{cm}$ with $A$ as the center.



3. Next, cut an arc of radius $50\text{cm}$ with $B$ as the center.


4. Join the intersection point $C$ with $A$ and $B$.


Now, using a protractor, measure $\angle BAC.$



$\angle BAC={90}^{\circ }$

$\therefore Area=\frac{1}{2}\times AB\times AC=\frac{1}{2}\times 40\times 30=600c{m}^2=6m^2$

Therefore, the area of the wooden piece will be $6m^2$.