Question

The area of a triangle is 150 cm2 and its sides are in the ratio 3 : 4 : 5. What is its perimeter?

Answer 1

➢Given :

• Area of a triangle = 150 cm².

• Ratio of its sides = 3 : 4 : 5.

➢To find :

• Find the perimeter of the triangle.

➢Solution :

• Let the first side be 3x.

• Let the second side be 4x

• Let the third side be 5x.

➡Here, all sides are different... So it is a scalene triangle.

• Semi - perimeter = 3x + 4x + 5x / 2

• Semi - perimeter = 6x.

• We know that,

[Refer to the 1sr Attachment ⬆]

➢According to the question :

• Area = 150 sq.cm.

[Refer to the 2nd Attachment⬆]

➡Therefore,

• Perimeter = a + b + c

• Perimeter = ( 15 + 20 + 25 ) cm.

• Perimeter = 60 cm.

➢Answer :

• So the perimeter of the triangle = 60 cm.

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Answer 2

Answer:

Thus, the perimeter of the triangle is $60cm$.

Step-by-step explanation:

Concept:

This formula's straight forward calculation supporting the length of a triangle's three sides makes it clear. We will use the area of triangle using heron's formula,

$A = \sqrt{s (s - a) (s - b) (s - c)}$

Semi perimeter$=\frac{a + b + c}{2}$

Given:

The area of triangle $= 150$ cm²

The sides are in ratio $= 3 : 4 : 5$

To find:

We have to search the perimeter of the given triangle.

Solution:

The area of triangle using heron's formula,

$A = \sqrt{s (s - a) (s - b) (s - c)}$

Semi perimeter$=\frac{a + b + c}{2}$

Assume that the ratios be $3x , 4x , 5x$.

$=\frac{3x + 4x + 5x}{2}$

$=\frac{12x}{2}\\= 6x$

Now apply Heron's formula,

$A = \sqrt{s (s - a) (s - b) (s - c)}$

$150 = \sqrt{6x (6x-3x) (6x-4x) (6x-5x)}$

$150 = \sqrt{6x (3x) (2x) (x)}\\150 = \sqrt{36x^{4}}$

150 = √36x⁴

$150 = 6x^{2}$

$\frac{150}{6} = x^{2}$

$25 = x^{2}$

$x=\sqrt{25} \\x=5$

Now, we have to find Perimeter as we get the value of $x$,

So ,

$3x = 3 * 5 = 15 cm\\4x = 4 * 5 = 20 cm\\5x = 5 * 5 = 25 cm$

Perimeter $=$ Adding all the three sides

$= 15 + 20 + 25$

$= 60 cm$

Therefore, The perimeter of triangle is $60$ cm.

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