Question

The lengths of the side of a  are in the ratio 3:4:5 and its perimeter in 180 cm. Find the area of the

.​

Answer 1

EXPLANATION.

$\sf : \implies \: let \: the \: length \: of \: sides \: be \: = x \\ \\ \sf : \implies \: its \: perimeter \: = 180 \: cm \\ \\ \sf : \implies \: 3x + 4x + 5x = 180 \\ \\ \sf : \implies \: 12x = 180 \\ \\ \sf : \implies \: x \: = \frac{180}{12} = 15 \: cm$

$\sf : \implies \: 3x = 3 \times 15 = 45 \\ \\ \sf : \implies \: 4x = 4 \times 15 = 60 \\ \\ \sf : \implies \: 5x = 5 \times 15 = 75 \\ \\ \sf : \implies \: s \: = \frac{a + b + c}{2} \\ \\ \sf : \implies \: s \: = \frac{45 + 60 + 75}{2} = \frac{180}{2} = 90$

$\sf : \implies \: by \: using \: herons \: formula \\ \\ \sf : \implies \: \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \sf : \implies \: \sqrt{90(90 - 45)(90 - 60)(90 - 75)} \\ \\ \sf : \implies \: \sqrt{90(45)(30)(15)} \\ \\ \sf : \implies \: \sqrt{1822500} \\ \\ \sf : \implies \: 1350 \: cm {}^{2}$

Answer 2

Answer:

Step-by-step explanation:

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

And perimeter of the triangle is 144cm.

So , 3x+4x+5x=144

       12x=144

         x=12

so, the sides are triangle are 3(12)=36cm, 4(12)=48cm , 5(12)=60cm

so , the longest side is 60 cm.

Area of triangle =  

s(s−a)(s−b)(s−c)

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here , s=72 and a=36, b=48 c=60

                          =  

72(72−36)(72−48)(72−60)

​  

 

                           =  

72(36)(24)(12)

​  

 

                            =  

746496

​  

 

                             = 864

So, the area of triangle is 864 cm  

2

 and the height corresponding to longest side h=  

60

2×864

​  

=

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