Question

Find the length represented by x for each pair of similar triangles

Answer 1

1)

Given:

Required:

We need to find the value of x.

Step-by-step explanation:

Recall that the corresponding sides of similar triangles are proportional.

12m and 6m are corresponding sides of the given similar triangles

16m and x are corresponding sides of the given similar triangles

The proportion of the sides can be written as follows.

`(12)/(6)=(16)/(x)`
`2=(16)/(x)`

Use the cross-product method.

`2x=16`
`(2x)/(2)=(16)/(2)`
`x=8m.`

2)

Given:

18cm and 30cm are corresponding sides of the given similar triangles.

x and 25 cm are corresponding sides of the given similar triangles.

Required:

We need to find the value of x.

Step-by-step explanation:

Recall that the corresponding sides of similar triangles are proportional.

The proportion of the sides can be written as follows.

`(18)/(30)=(x)/(25)`

Multiply both sides of the equation by 25.

`(18*25)/(30)=(x)/(25)*25`
`15=x`
`x=15cm`

3)

Given:

x and 21m are the corresponding sides of the given similar triangles.

32m and 24m are the corresponding sides of the given similar triangles.

Required:

We need to find the value of x.

Step-by-step explanation:

Recall that the corresponding sides of similar triangles are proportional.

The proportion of the sides can be written as follows.

`(x)/(21)=(32)/(24)`

Multiply both sides of the equation by 21.

`(x)/(21)*21=(32)/(24)*21`
`x=28m`

4)

Given:

12in and 15in are the corresponding sides of the given similar triangles.

x and 40in are the corresponding sides of the given similar triangles.

Required:

We need to find the value of x.

Step-by-step explanation:

Recall that the corresponding sides of similar triangles are proportional.

The proportion of the sides can be written as follows.

`(12)/(15)=(x)/(40)`

Multiply both sides of the equation by 40.

`(12)/(15)*40=(x)/(40)*40`
`x=32in`

Final answer:

1)

`x=8m.`

2)

`x=15cm`

3)

`x=28m`

4)

`x=32in`