Question

The sides of the triangle are in the ratio is \[2:3:4\]. If the perimeter of the triangle is 27 cm, find the length of each side?

Answer 1

Hint: Here in this question, we have to find the length of each side of the triangle using the given ratios and the perimeter of the triangle. To solve this, consider the length of the triangles are \[2x\], \[3x\], and \[4x\] which sum of these three length is equal to the perimeter on substituting the value of perimeter and by further simplification using basic arithmetic operation to get the required solution.

Complete step-by-step answer:
Consider the triangle, \[\Delta \,ABC\] given the ratio of the sides of a triangle is \[2:3:4\] then the length of the each side of an triangle is \[AB = 2x\], \[AC = 3x\] and \[BC = 4x\] respectively.

Then, given the perimeter of the triangle is 27cm,
Here, we have to find the exact length of the each side of triangle.
As we know, perimeter can be defined as the path or the boundary that surrounds a shape. It can also be defined as the length of the outline of a shape.
Therefore, in \[\Delta \,ABC\] the perimeter is:
\[ \Rightarrow \,\,\,P = AB + AC + BC\]
\[ \Rightarrow \,\,\,P = 2x + 3x + 4x\]
Given perimeter \[P = 27cm\], on substituting we have
\[ \Rightarrow \,\,\,27 = 2x + 3x + 4x\]
On substituting, we get
\[ \Rightarrow \,\,\,27 = 9x\]
Divide both side by 9, then
\[ \Rightarrow \,\,\,\dfrac{{27}}{9} = x\]
\[ \Rightarrow \,\,\,3 = x\]
or
\[ \Rightarrow \,\,\,x = 3\]
Hence, the length of each side of an \[\Delta \,ABC\] is:
\[ \Rightarrow \,\,\,AB = 2x = 2\left( 3 \right) = 6cm\]
\[ \Rightarrow \,\,\,AC = 3x = 3\left( 3 \right) = 9cm\]
\[ \Rightarrow \,\,\,BC = 4x = 4\left( 3 \right) = 12cm\]
Therefore, the length of each side of a triangle is \[6cm\], \[9\,cm\] and \[12\,cm\].

Note: While determining the length or perimeter of shapes we use the formula. The unit for the perimeter will be the same as the unit of the length of a side or triangle. Whereas the unit for the area will be the square of the unit of the length of a triangle. We should not forget to write the unit.