If triangle cfh is similar to triangle tdm with a scale factor of 4: 5 find the perimeter of cfh

Given: If triangle CFH is similar to triangle TDM with a scale factor of 4: 5.

Similar triangle states that the two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

then by definition, we have;

 .....[1]

From the figure, we have;

CF = x +7 , FH = x-1 , CH = x+3 , TD = 2x -13 , DM = x+6 and TM = x+ 11

Solve for x;

[1] ⇒

Substitute the value of CF and TD to solve for x;

By cross multiply we get;

Using distributive property :

5x + 35 = 8x - 52

Subtract 35 on both sides we get;

5x + 35 -35 = 8x - 52 -35

Simplify:

5x = 8x - 87

Subtract 8x on both sides we get;

5x -8x = 8x -87 -8x

Simplify:

-3x = -87

Divide both sides by -3 we get;

x = 29

To find the perimeter of triangle CFH;

Sides are:

CF = x + 7 = 29 + 7 = 36 units

CH = x+3 = 29 +3 = 32 units

FH = x -1 = 29 -1 = 28 cm.

Perimeter of any triangle is the sum of all the sides of the triangle.

Perimeter of triangle CFH = CF + CH + FH = 36 + 32 + 28 = 96 units

therefore, the perimeter of triangle CFH is, 96 units.

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