Question

Plzzzzzz helppppp meeee !!!

Answer 1

Answer:

Corresponding side of AB is FE

Corresponding side of CB is DE

Corresponding side of AC is FD

$k =2$

$DE = 6$

$FD=10$

Step-by-step explanation:

Given

$\triangle ABC$ and $\triangle FED$

See attachment for triangles

Solving (a): Corresponding side of AB

Going by the names of the triangle, the corresponding sides are:

AB and FE; CB and DE; AC and FD

Hence, the corresponding side of AB is FE

Solving (b): Corresponding side of CB

This has been solved in (a) above.

The corresponding side of CB is DE

Solving (c): Corresponding side of AC

This has been solved in (a) above.

The corresponding side of AC is FD

Solving (d): Scale factor from ABC to FED

To do this, we simply divide the lengths of corresponding sides.

The scale factor k is:

$k = \frac{FE}{AB}$

$k = \frac{8}{4}$

$k =2$

Solving (e): Length of DE

We make use of the scale factor calculated in (d) above

$k = \frac{DE}{CB}$

$2 = \frac{DE}{3}$

$DE = 2 * 3$

$DE = 6$

Solving (f): Length of FD

Using Pythagoras:

$FD^2 = DE^2 + EF^2$

$FD^2 = 6^2 + 8^2$

$FD^2 = 100$

$FD = \sqrt{100$

$FD=10$