Question

The lengths of the sides of a triangle are in the ratio of 3: 4 : 5 and the perimeter of the triangle is 108cm. The measure of the longest side is _______ m.​

Answer 1

Step-by-step explanation:

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

And perimeter of the triangle is 108cm.

So , 3x+4x+5x=108

12x=130

x=12

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

so , the longest side is 60 cm.

Answer 2

To find : measure of longest side of triangle .

Given : The lengths of the sides of a triangle are in the ratio of $3: 4 : 5$ and the perimeter of the triangle is $108\ cm.$

Solution :

• As per given data we know that  lengths of the sides of a triangle are in the ratio of $3: 4 : 5$ and perimeter of the triangle is $108\ cm.$  
• Let , $3x,4x,5x$ be the sides of triangle .
• If $a,b,c$ are the sides of triangle then perimeter is given by ,  
• Perimeter of triangle  =$a + b+c$
• Substituting the values in the above formula to find length of sides of triangle .

        $108 =3x + 4x + 5x \\108 =12x \\x = 9$

• Now , sides of triangle are:

       $3x =3\times 9 =27\ cm \\4x = 4\times 9 =36\ cm \\5x = 5\times 9 =45\ cm$

Hence , measure of longest side of triangle is $45\ cm$ .