Question

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.

6.33

7.2

5

8

Answer 1

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

`(AB)/(XY) =(BC)/(YZ) =(AC)/(XZ)`

`(2)/(4) =(x+5)/(5x-5)`

`10x-10=4x+20 6x=30,x=5`

the value of x is 5 is found out by using ratio of corresponding sides are equal .

Answer 2

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

`(AB)/(XY) =(BC)/(YZ)=(AC)/(XZ)`

AB=2, BC=x+5, XY=4 ,YZ=5x-5

Let us use

`(AB)/(XY) =(BC)/(YZ)`

`(2)/(4) =(x+5)/(5x-5)`

To get rid of fractions, Let us multiply by 4(5x-5)

`4(5x-5)(2)/(4) =4(5x-5)(x+5)/(5x-5)`

`1(5x-5)(2)/(1) =4(x+5)/(1)`

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,
`(6x)/(6) =(30)/(6)`

So,
`(1x)/(1) =(5)/(1)`

x=5

So, the value of x=5 Answer