If △QRS ≅△TUV, then we know that the corresponding sides are proportional. Therefore, we can set up the following equation:
QS/TV = (4w+16)/(6w-8)
To solve for QS and TV, we can cross multiply:
QS * (6w-8) = TV * (4w+16)
Expanding this equation, we get:
6w * QS - 8 * QS = 4w * TV + 16 * TV
Simplifying further, we have:
6wQS - 8QS = 4wTV + 16TV
Now, let's solve for QS. We can factor out QS on the left-hand side:
QS(6w - 8) = 4wTV + 16TV
Dividing both sides by (6w - 8), we get:
QS = (4wTV + 16TV)/(6w - 8)
To find the length of QS, we need to know the length of TV. However, we are not given the value of w, so we cannot solve for TV and QS at this time.
Given △QRS ≅△TUV , QS = 4w+16 and TV = 6w - 8, find the length of TV and QS. Show all the steps that you used to solve this problem in order to earn full credit. (2 points)
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