Question

The sides of a triangle are in the ratio of 3 : 4 : 5. If its perimeter is 36 cm, then what is its area?


32 sq. cm

54 sq. cm

67 sq.cm

72 sq.cm

​

Answer 1

Given :

• The sides of a triangle are in the ratio of 3 : 4 : 5.

• Its perimeter is 36 cm.

To find :

• Area of triangle =?

Step-by-step explanation :

Let, the sides of a triangle are 3x, 4x and 5x.

It is Given that :

Its perimeter is 36 cm. [Given]

So, Sum of all sides of triangle = 36 cm.

Substituting the values, we get,

➮ 3x + 4x + 5x = 36

➮ 12x = 36

➮ x = 36/12

➮ x = 3.

Therefore, We get the value of, x = 3 cm.

Hence,

3x = 3 × 3 = 9 cm

4x = 4 × 3 = 12 cm

5x = 5 × 3 = 15 cm

Now,

We know that, it is an right angled triangle because the sum of squares of two smaller sides is equal to the square of larger sides.

9² + 12² = 15²

15² = 225

Here, the length of hypotenuse is 15 cm.

We know that,

Area of right angled triangle = 1/2 × base × height

Substituting the values in the above formula, we get,

= 1/2 × 9 × 12

= 9 × 6

= 54.

Therefore, Area of triangle = 54 cm².

Answer 2

✯✯ QUESTION ✯✯

The sides of a triangle are in the ratio of 3 : 4 : 5. If its perimeter is 36 cm, then what is its area?

32 sq. cm

54 sq. cm

67 sq.cm

72 sq.cm

━━━━━━━━━━━━━━━━━━━━

✰✰ ANSWER ✰✰

$\longmapsto\tt{Let\:the\:length\:of\:1st\:Side=3x}$

$\longmapsto\tt{Let\:the\:length\:of\:2nd\:Side=4x}$

$\longmapsto\tt{Let\:the\:length\:of\:3rd\:Side=5x}$

$\longmapsto\tt{Perimeter=36cm}$

➥A.T.Q : -

$\longmapsto\tt{3x+4x+5x=36}$

$\longmapsto\tt{12x=36}$

$\longmapsto\tt{x=\cancel\dfrac{36}{12}}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{x}\orange{=}\purple{3}}}$

☛So , Value of x is 3...

➥Now ,

$\longmapsto\tt{Ist\:Side = 3(3)}$

$\longmapsto\tt{9cm}$

$\longmapsto\tt{2nd\:Side=4(3)}$

$\longmapsto\tt{12cm}$

$\longmapsto\tt{3rd\:Side=5(3)}$

$\longmapsto\tt{15cm}$

➙Firstly we will find the length of Hypotenuse :

$\longmapsto\tt{{c}^{2} = \sqrt{{a}^{2}+{b}^{2}}}$

➥Putting Values : -

$\longmapsto\tt{{15}^{2}=\sqrt{{9}^{2}+{12}^{2}}}$

$\longmapsto\tt{{15}^{2} = \sqrt{81 + 144}}$

$\longmapsto\tt{{15}^{2}=\sqrt{225}}$

$\longmapsto\tt{15cm}$

☛Length of Hypotenuse is 15cm...

➥Now ,

$\longmapsto\tt{Base= 9cm}$

$\longmapsto\tt{Height=12cm}$

➥Using Formula : -

$\longmapsto\tt{\small{\boxed{\bold{\bold{\red{\sf{Area\:of\:Triangle=\dfrac{1}{2}\times{b}\times{h}}}}}}}}$

➙Putting Values : -

$\longmapsto\tt{\dfrac{1}{\cancel{2}}\times{9}\times{\cancel{12}}}$

$\longmapsto\tt{9\times{6}}$

$\longmapsto\tt{\large{\boxed{\bold{\bold{\green{\sf{{54cm}^{2}}}}}}}}$

☛Area of Triangle is 54cm².....

➥Option B) 54cm² is Correct...