Question

In a $\Delta ABC$ of area 12 square centimeters, AB and BC are perpendicular sides. The length of AB is 6 centimeters. Which of the following options is true?

• A. $AC=7.2\text{cm}$ and Perimeter of $\Delta ABC=17.2\text{cm}$
• B. $AC=7.2\text{cm}$ and Perimeter of $\Delta ABC=10.2\text{cm}$
• C. $AC=7\text{cm}$ and Perimeter of $\Delta ABC=17.2\text{cm}$
• D. $AC=6.2\text{cm}$ and Perimeter of $\Delta ABC=17.2\text{cm}$

Answer 1

The correct option is A $AC=7.2\text{cm}$ and Perimeter of $\Delta ABC=17.2\text{cm}$

We know, AB = 6 cm and AB and BC are perpendicular sides.
Area of a right triangle $=\frac{1}{2}\times$ product of the perpendicular sides
$\Rightarrow 12=\frac{1}{2}\times AB\times BC$
$\Rightarrow 12=\frac{1}{2}\times 6\times BC$
$\Rightarrow 12=3\times BC$
$\Rightarrow BC=\frac{12}{3}=4\text{cm}$
Let’s construct triangles taking these measures of AB and BC, and measure the length of AC.
Since it is given that AB and BC are perpendicular to each other, hence $\angle B={90}^{\circ }$.
Steps:
1. Let us first draw a line segment AB of length $6\text{cm}$ using a ruler.
2. Now, let’s draw ray BX making an angle ${90}^{\circ }$ with AB.
3. With center at B and radius 4 cm, draw an arc on ray BX which will be the third vertex of the triangle, i.e., C.

4. Draw the third line of the triangle by joining C and A.

5. Measuring AC using ruler we get, $AC=7.2\text{cm}$
Perimeter $=AB+BC+AC=6+4+7.2=17.2\text{cm}$