Question

The area of triangle is 150 cm2 and it's sides is 3:4:5. what is it' perimeter???​

Answer 1

Answer :-

$\large{\boxed{\underline{\sf Perimeter = 60 cm}}}$

Explanation :-

Given :

• Area of triangle - 150 cm²
• Ratio of it's sides - 3 : 4 : 5

To find :

The perimeter of the triangle

Solution :

Let the first side be 3x

the second side be 4x

and the third side be 5x

(Since all the sides are different, it's a scalene triangle)

Now,

$\sf\longrightarrow Semi - perimeter = \dfrac{3x + 4x + 5x}{2}$

$\sf\longrightarrow Semi - perimeter = 6x$

We know that,

$\sf\longrightarrow\sqrt{s(s - c)(s - b)(s - c)} = 150$

According to question,

$\sf\longrightarrow Area = 150 sq.cm$

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

$\sf\longrightarrow\sqrt{6x × 3x × 2x × x} = 150$

$\sf\longrightarrow\sqrt{2 × 3 × x × 3 × x × 2 × x × x} = 150$

$\sf\longrightarrow 2 × 3 × x × x = 150$

$\sf\longrightarrow 6{x}^{2} = 150$

$\sf\longrightarrow {x}^{2} = \dfrac{150}{6}$

$\sf\longrightarrow {x}^{2} = 25$

$\sf\longrightarrow x = \sqrt{25}$

$\sf\therefore x = 5$

Therefore,

The first side => 3 × 5 = 15 cm

The second side => 4 × 5 = 20 cm

The third side => 5 × 5 = 25 cm

Now, We know that,

$\large{\underline{\boxed{\sf Perimeter = a + b + c}}}$

$\sf\longrightarrow Perimeter = a + b + c$

$\sf\longrightarrow Perimeter = (15 + 20 + 25) cm$

$\sf\longrightarrow Perimeter = 60 cm$

Hence, the perimeter of the triangle is 60 cm respectively.

Answer 2

Answer:

60

Step-by-step explanation:

3x+4x+5x=perimeter

12x=p ----------1

150=root(s(s-3x)(s-4x)(s-5x))

22500=6x*3x*2x*x

22500=36x*x^4

625=x^4

x=5

by 1

p=60

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