Question

Construct a $\angle ABC$ , where $AB=2.7\text{cm},BC=3.7\text{cm}$, and the right angle is at $B$. Also, find the approximate length of the side $AC$.

• A. $3.2\text{cm}$
• B. $4\text{cm}$
• C. $3.8\text{cm}$
• D. $4.6\text{cm}$

Answer 1

The correct option is D $4.6\text{cm}$

Given:

• $AB=2.7\text{cm}$
• $BC=3.7\text{cm}$
• $\angle ABC={90}^{\circ }$

We can construct the triangle using the SAS criterion.
The first step is to draw the base $AB$ of length $2.7\text{cm}$ using a ruler.



At $B$, draw a ray, $BX$, making an angle ${90}^{\circ }$ with $BA$.

Now, with $B$ as the center and radius $3.7\text{cm}$, draw an arc intersecting ray $BX$ at point $C$


Next, join $AC$ to complete the triangle.

Measuring the length of $AC$ using a ruler, we get $AC\approx 4.6\text{cm}$.