Answer:
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;
[tex]\frac{CF}{TD}= \frac{FH}{DM} =\frac{CH}{TM}= \frac{4}{5}[/tex] .....[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] ⇒ [tex]\frac{CF}{TD} =\frac{4}{5}[/tex]
Substitute the value of CF and TD to solve for x;
[tex]\frac{x+7}{2x-13} = \frac{4}{5}[/tex]
By cross multiply we get;
[tex]5 (x+7) = 4(2x-13)[/tex]
Using distributive property : [tex]a\cdot(b+c) = a\cdot b + a\cdot c[/tex]
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.
