Question

ABC and DEF are two similar triangles. Angle ABC = Angle DEF Angle ACB = Angle DFE Work out the length of BC.

Answer 1

To find the length of BC in similar triangles, we can use the proportion of their corresponding sides.

Step-by-step explanation:

In the given question, ABC and DEF are two similar triangles. It is given that Angle ABC is equal to Angle DEF and Angle ACB is equal to Angle DFE. Since the triangles are similar, their corresponding sides are proportional to each other. So, we can set up the proportion:

AB/DE = BC/EF

Since we need to find the length of BC, we can rearrange the proportion to isolate BC:

BC = (AB * EF)/DE.

Therefore, the length of BC is equal to the product of AB and EF divided by DE.

Answer 2

The length of BC is 9.33 cm.

In similar triangles, corresponding sides are the sides that are opposite to congruent angles.

From the given information, we know that angle ABC is equal to angle DEF, and angle ACB is equal to angle DFE.

Therefore, the corresponding sides are:

BC corresponds to EF (opposite to equal angles ABC and DEF)

AC corresponds to DF (opposite to equal angles ACB and DFE)

Set up a Proportion:

Since the triangles are similar, the ratios of corresponding sides are equal.

We can set up a proportion using the known side lengths:

AC/DF = BC/EF

Substitute Known Values:

Plug in the given side lengths:

15 cm / 14 cm = DF / 15 cm

Cross-multiply to isolate DF:

15 cm * 14 cm = 15 cm * DF

Simplify:

210 cm² = 15 cm * DF

Divide both sides by 15 cm:

DF = 210 cm² / 15 cm

DF = 14 cm

Now, since the scale factor is mentioned as
`$(2)/(3)$`, the length of
`$\mathrm{BC}$` (which corresponds to EF) would be:

`\begin{aligned}& B C=D F * (2)/(3) \\& B C=14 \mathrm{~cm} * (2)/(3) \\& B C=9.33 \mathrm{~cm}\end{aligned}`

Complete Question:

`$A B C$` and
`$D E F$` are two similar triangles.
Angle
`$A B C=$` Angle
`$D E F$`
Angle
`$A C B=$` Angle
`$D F E$`

Work out the length o f
`$BC$`.