we have given the two triangles which is similar.
we know that in similar triangles ratio of corresponding sides are equal.
in triangle ABC and XYZ
[tex] \frac{AB}{XY} =\frac{BC}{YZ} =\frac{AC}{XZ} [/tex]
[tex] \frac{2}{4} =\frac{x+5}{5x-5} [/tex]
[tex] 10x-10=4x+20 6x=30,x=5 [/tex]
the value of x is 5 is found out by using ratio of corresponding sides are equal .
Triangle ABC is similar to triangle XYZ. Side AB measures 2, side BC measures x + 5, side CA measures x + 7, side XY measures 4 and side YZ measures 5x – 5. Find the value of x.
As, triangle ABC is similar to triangle XYZ
So, the ratios of sides is equal
[tex] \frac{AB}{XY} =\frac{BC}{YZ}=\frac{AC}{XZ} [/tex]
AB=2, BC=x+5, XY=4 ,YZ=5x-5
Let us use
[tex] \frac{AB}{XY} =\frac{BC}{YZ} [/tex]
[tex] \frac{2}{4} =\frac{x+5}{5x-5} [/tex]
To get rid of fractions, Let us multiply by 4(5x-5)
[tex] 4(5x-5)\frac{2}{4} =4(5x-5)\frac{x+5}{5x-5} [/tex]
[tex] 1(5x-5)\frac{2}{1} =4\frac{x+5}{1} [/tex]
2(5x-5)=4(x+5)
10x-10=4x+20
To solve for x, Let us collect x terms
So, Let us subtract 4x from both sides
10x-4x-10=4x-4x+20
6x-10=0+20
Adding 10 on both sides
6x-10+10=20+10
6x+0=30
So, 6x=30
To, solve for x, Let us divide by 6 on both sides
So, [tex] \frac{6x}{6} =\frac{30}{6} [/tex]
So, [tex] \frac{1x}{1} =\frac{5}{1} [/tex]
x=5
So, the value of x=5 Answer
