Question

In a right triangle $ABC$ of area $24{\text{unit}}^2,$ $AB\text{and BC}$ are perpendicular sides. The length of $AB$ is $6\text{units}$. Construct the triangle and find its perimeter.

• A. 24

Answer 1

The correct option is A 24
Given:

• AB = $6\text{units}$
• $AB\text{and}BC$ are perpendicular sides.
• $AB$ is one of the perpendicular sides.
• Area = $24{\text{units}}^2$

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

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

Therefore, $24=\frac{1}{2}\times 6\times BC\Rightarrow BC=8\text{units}$

Constructing $\Delta ABC$ using the SAS criterion, we have:

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 $B$ using a protractor. $\angle ABC={90}^{\circ }$


3. Cut an arc of $8\text{ft}$ with $B$ as the center.


4. Join $AC$.

Now, measuring the length of side $AC$ using a ruler, we get: $AC=10\text{ft}$

Perimeter of $\Delta ABC$
$=AB+BC+AC=6+8+10=24\text{ft}$