Question

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Given  ΔQRS≅ΔTUV ,  QS=3v+2  and  TV=7v−6 , find the length of QS and TV.

Answer 1

By setting the expressions for QS (3v+2) and TV (7v-6) equal because ΔQRS and ΔTUV are congruent, we solve for v and find that both QS and TV equal 8 units in length.

Step-by-step explanation:

Since triangles ΔQRS and ΔTUV are congruent (ΔQRS≅ΔTUV), corresponding sides are equal in length. This means that QS is equal in length to TV. Therefore, the expressions for QS (3v+2) and TV (7v-6) are equal, and we can set them equal to each other to solve for v:

3v + 2 = 7v - 6

To find the value of v, we rearrange the equation:

4v = 8

Divide both sides by 4:

v = 2

Now we substitute v = 2 into the original expressions to find the lengths of QS and TV:

QS = 3(2) + 2 = 6 + 2 = 8

TV = 7(2) - 6 = 14 - 6 = 8

Hence, the length of QS and TV is 8 units each.