Question

In a right triangle $ABC$ of area $6c{m}^2,AB\text{and BC}$ are perpendicular sides. The length of $AB$ is $3\text{cm}$. Construct a triangle and find its perimeter.

• A. $12\text{cm}$
• B. $15\text{cm}$
• C. $10\text{cm}$
• D. $20\text{cm}$

Answer 1

The correct option is A $12\text{cm}$

Given:

• AB = $3\text{cm}$
• $AB\text{and}BC$ are perpendicular sides.
• $AB$ is one of the perpendicular sides.
• Area = $6c{m}^2$

Let’s assume $BC$ is the other perpendicular side.

The area of a right triangle = $\frac{1}{2}\times$ Product of the perpendicular sides =$\frac{1}{2}\times AB\times BC$

Therefore, $6=\frac{1}{2}\times 3\times BC\Rightarrow BC=4\text{cm}$

Constructing $△ABC$ using the SAS criteria, we get:

1.First, let’s draw the line segment $AB$.


2. In the question, $AB\text{and}BC$ are perpendicular sides. Let’s draw a ${90}^{\circ }$ angle $B.\angle ABC={90}^{\circ }$


3. Cut an arc of $4\text{cm}$ with $B$ as the center.


4. Join $AC$.

Now measure the length of side $AC$ using a ruler, we get: $AC=5\text{cm}$

Perimeter of $△ABC=AB+BC+AC=3+5+4=12\text{cm}$