Question

For ΔQRS use the Triangle Proportionality Theorem to solve for x.

After you have solved for x, what is the Perimeter of ΔQRS?

Can you answer, show work, and explain it to me?
I struggle a lot with this type of math, thank you.

Answer 1

Thanks for the points :3

Answer 2

The x is 347/196 . The Perimeter of ΔQRS is 962/196 .

Triangle Proportionality Theorem: If a line parallel to one side of a triangle intersects the other two sides at different points, then it divides the remaining two sides proportionally.

To solve for x:

Step 1: Identify the parallel lines in the triangle. In this case, lines QR and ST are parallel.

Step 2: Set up two proportions, one for each pair of corresponding sides of the two triangles.

Proportion 1:

QS/QT = SR/ST

​Proportion 2:

QS/QT = QR/RS

​Step 3: Substitute in the known values and solve for x.

Proportion 1: 13/x = 7/21

x⋅7=13⋅21

x⋅7=273

x = 273/ 7

​Proportion 2: 13/x = 2x-2/17

​17x−34=213x

196x=347

x= 347/ 196

​Since both proportions yield the same value for x, we know that our answer is correct.

Therefore, x = 347/ 196

To find the perimeter of ΔQRS:

Perimeter = QS + QR + SR

Perimeter = 13 + (2x - 2) + 7

Perimeter = 13 + 2x - 2 + 7

Perimeter = 2x + 18

Substituting x = 347/ 196​ , we get:

Perimeter = 2( 347/196 ) + 18

Perimeter = 694/196 + 18

Perimeter = 962/196