The area of a triangle is 12 cm^2 and its sides are in the ratio 2 : 3 : 4. what is its perimeter?

Question 4 Heron's Formula - Exercise 12.3

Answer:

According to the question,

Perimeter of the isosceles triangle = 32 cm

It is also given that,

Ratio of equal side to base = 3 : 2

Let the equal side = 3x

So, base = 2x

Perimeter of the triangle = 32

⇒ 3x + 3x + 2x = 32

⇒ 8x = 32

⇒ x = 4.

Equal side = 3x = 3×4 = 12

Base = 2x = 2×4 = 8

The sides of the triangle = 12cm, 12cm and 8cm.

Let a = 12, b = 12, c = 8

s = (a + b + c)/2

⇒ s = (12 + 12 + 8)/2

= 32/2

= 16.

Area of the triangle = √s(s-a)(s-b)(s-c)

= √16(16-12)(16-12)(16-8)

= √16×4×4×8

= 32√2 cm²

Video transcript

"hello students and welcome back on a lido doubt solving session and in today's session we are going to find it out the area of isosceles triangle right so i will read the question first the perimeter of an iso scale triangle is 32 centimeter the ratio of equal side to its base is 3 as to 2 find the area of the triangle right now quickly solve this and find out the area okay so first we will note down the given data right so q1 [Music] okay the perimeter is given here right perimeter perimeter is equals to 32 centimeter right okay and the ratio of equal side to its base is given so ratio of equal side to base is equals to 3s to 2 right so let's consider let base is equals to 2x and equal side equal side is equals to three x right okay so now um what we'll do okay apply the formula perimeter here so perimeter is equals to okay addition of all the sides right that is a plus b plus c okay and that's why okay perimeter is okay 32 centimeter which is given here okay base is 2x plus okay equal sides are 3x plus 3x right that's why 8x is equals to 32 okay and from this we will get the value of x which is equals to 4 right okay now by putting this value okay we will get the base of the triangle as well as equal sides right so that's why base is equals to base was 2 x is equal that means okay x is 4 so that's why okay base will be the 8 centimeter right similarly okay another sides okay that is side b okay and side c are same right so side b is equals to side c which is equals to 3 x okay that means 3 multiplied by four is equal to 12 x okay 12 centimeter okay so basically okay we get the value of a you get the value of b and we get the value of c right now find it out the same perimeter so semi perimeter semi perimeter is equals to a plus b plus c divided by 2 or it is simply perimeter by 2 right perimeter by 2 and that's why perimeter is 32 so that's why semi perimeter will be the 16 centimeter right okay now use the formula okay apply the value and find out the answer so area of the triangle is area of the triangle is equals to under root of s into s minus a in bracket s minus b and s minus c all right s is semi perimeter here okay so by putting the value same perimeter is 16 so 16 okay a is 8 so that is that means 16 minus 8 okay 16 minus 12 and 16 minus 12 right okay now we'll quickly solve this we'll do the calculation 16 16 minus 8 is equals to 8 okay 16 minus 12 that means 4 and again 16 minus 12 that means 4 right okay now what we will do okay as we know that 16 4 and 4 okay these are the square numbers right so we can take them okay um take out from the under root right so 16 will become 4 and this 4 will become 2 this again 4 will become two right okay so okay here what i will do i will take out this from the like from the square root so 16 will become 4 okay multiplied by this 4 into 4 that is 16 ticket so again it will be 4 so 4 into 4 and 2 under root of 8 right okay now what i will do okay i will express this 4 into 4 that is 16 okay under root of 8 is also 4 multiplied by 2 right okay and that's why the area will be area will be okay we will take out 4 from the square root so it is 2 so 69 2 is equals to 32 times under 2 centimeter square right so that will be the final answer that will be the area of triangle so that's all about today's session i hope you understood this if you have any doubt please leave the comment below and please do subscribe to this channel so that you will get a notification for upcoming video thanks for watching this video bye"

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