Question

Triangles ABC and DFG are given. Find the lengths of all other sides of these triangles if: b ∠A≅∠D, AB·DG=AC·DF, AC=7 cm, BC=15 cm, FG=20 cm, and DF-AB=3 cm.

Answer 1

Answer:

$AB=9cm$ and  $DG=\frac{28}{3}cm$

Step-by-step explanation:

Given triangles ABC and DFG such that AB·DG=AC·DF and ∠A≅∠D

and AC=7 cm, BC=15 cm, FG=20 cm, and DF-AB=3 cm.

We have to find all other sides of triangle.

Now, AB·DG=AC·DF

⇒ $\frac{AB}{DF}=\frac{AC}{DG}$

and ∠A≅∠D

Hence, by SAS rule ΔABC~ΔDFG

⇒ $\frac{AB}{DF}=\frac{AC}{DG}=\frac{BC}{GF}$

⇒ $\frac{AB}{3+DF}=\frac{7}{DG}=\frac{15}{20}$

⇒  $\frac{AB}{3+DF}=\frac{15}{20}$  

⇒ 20AB=45+15AB ⇒ 5AB=45 ⇒ AB=9 cm

Also, $\frac{7}{DG}=\frac{15}{20}$

⇒ $DG=\frac{28}{3}cm$

Answer 2

The measure of the length DG is 28/3cm and AB is 9cm.

What is the similarity theorem of a triangle?

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

By using the similarity theorem of a triangle:

$\rm\dfrac{AC}{BC}=\dfrac{DG}{FG}\\\\\ \dfrac{7}{15}=\dfrac{DG}{20}\\\\7 \times 20=DG\times 15\\\\140=15 DG\\\\DG=\dfrac{140}{15}\\\\DG=\dfrac{28}{3}$

And the measure of AB is;

DF - AB = 3 cm

AB = 3+6 = 9cm

Hence, the measure of the length DG is 28/3cm and AB is 9cm.

To know more about the Similarity theorem click the link given below.

brainly.com/question/11977990