Question

A triangle has sides 1/2: 1/3: 1/4. perimeter of triangle 52 cm. smallest side of length.

Answer 1

Let the sides be 1/2x,1/3x,1/4x
Perimeter = a+b+c
52cm=1/2x+1/3x+1/4x
52cm=(6x+4x+3x)/12
52=13/12x
52*12/13=x
4*12=x=48
Sides are (1/2)*48=24cm;(1/3)*48=18cm;(1/4)*48=12cm
.
. . 12cm is the smallest side

Answer 2

The length of the smallest side is 12cm

Given

• sides 1/2: 1/3: 1/4
• perimeter of triangle 52 cm

To find

• smallest side of length.

Solution

we are provided with the sides of the triangle in ratios and are asked to find the smallest side of the given triangle.

let X be the common factor that has been cancelled out to form the ratio, therefore,

x/2 + x/3 + x/4 = 52 { the sum of the three sides of a triangle would give perimeter}

or, (6x+ 4x + 3x)/12 = 52

or, 13x/12 = 52

or, 13x = 624

or, x = 48cm

therefore the sites of the triangle would be,

x/2 = 48/2

or, 24cm

x/3 = 48/3

or, 16cm

x/4 = 48/4

or, 12cm

Therefore, the length of the smallest side is 12cm