Question

Area of a right triangle is 30 cm2

. If one of its legs is 12 cm long, its perimeter is




(1) 17 cm

(2) 20 cm



(3) 60 cm

(4) 30 cm


​

Answer 1

Answer :-

• Option 4 is the correct one.
• The perimeter of the triangle is 30 cm.

Given :-

• Area of a right angled triangle is 30 cm².
• One of its legs is 12 cm long.

To find :-

• The perimeter of the triangle.

Step-by-step explanation :-

• In this question, the area of a right angled triangle has been given to us. It has also been given that one of its legs is 12 cm long. We have to find it's perimeter. For this, we first have to find the height of the triangle by applying the formula required for finding the area of a triangle. Then, we will use the height to find the hypotenuse (Third side) of the triangle by using the Pythagoras theorem, then finally, we will find the perimeter of the triangle using the three sides.

Let's proceed!

Calculations :-

We know that :-

Area of a triangle = $\underline{\boxed{\tt\dfrac{1}{2} \times base \times height}}$

Here,

Area = 30 cm².

One of the legs = 12 cm.

So, let the base be 12 cm and the height be h.

Now, substituting the values in the given formula,

$\sf 30 = \dfrac{1}{2} \times 12 \times h$

Multiplying 12 by h,

$\sf30 = \dfrac{1}{2} \times 12h$

Multiplying $\sf \dfrac{1}{2}$ by 12h,

$\sf30 = \dfrac{12h}{2}$

Transposing 2 from LHS to RHS, changing it's sign,

$\sf30 \times 2 = 12h$

Multiplying the numbers,

$\sf60= 12h$

Transposing 12 from LHS to RHS, changing it's sign,

$\sf \dfrac{60}{12} = h$

Dividing 60 by 12,

$\sf5 = h.$

• So, we have the height now, which can also be taken as the second leg of the triangle.

• We know that the third side of the triangle is called the hypotenuse, while the other two sides are called the legs.

• So that means, we have to find out the measure of the hypotenuse to find the perimeter, since we can only find the perimeter of a triangle when we know the measure of all the three sides.

We can find the hypotenuse using the Pythagoras theorem.

• Pythagoras theorem :- In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

So now let's use this theorem to find the hypotenuse.

Let the hypotenuse be x.

Substituting the given values in the formula,

$\bf{x}^{2} = {12}^{2} + {5}^{2}$

$\bf{x}^{2} = 144 + 25$

$\bf {x}^{2} = 169$

$\bf x = \sqrt{169}$

$\bf x = 13.$

So, the hypotenuse = 13 cm.

Now, we have the measures of all the three sides of the triangle, so let's find its perimeter.

We know that :-

Perimeter of a triangle = Sum of all sides.

Here, the sides are 12 cm, 5 cm and 13 cm.

Therefore,

$\tt Perimeter = 12 \: cm + 5 \: cm + 13 \: cm = 30 \: cm.$

Thus, the perimeter of the triangle is 30 cm.

Hence, option 4 is correct.