Given △QRS ≅△TUV%0D%0A△%0D%0A%0D%0A%0D%0A%0D%0A %0D%0A≅%0D%0A△%0D%0A%0D%0A%0D%0A%0D%0A, 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.
To find the length of TV and QS, we need to set up an equation using the given information.
From the congruence of triangles △QRS ≅ △TUV, we can conclude that the corresponding sides of both triangles are equal. Therefore, we have:
QS = TU (corresponding sides are equal)
4w + 16 = 6w - 8 (substituting the given expressions for QS and TV)
Next, we solve the equation for w:
4w + 16 = 6w - 8 (subtracting 4w from both sides to isolate the w term)
16 = 2w - 8 (adding 8 to both sides)
24 = 2w (dividing both sides by 2)
w = 12
Now that we know the value of w, we can substitute it back into the expressions for QS and TV to find their lengths:
QS = 4w + 16
QS = 4(12) + 16
QS = 48 + 16
QS = 64
TV = 6w - 8
TV = 6(12) - 8
TV = 72 - 8
TV = 64
Therefore, the length of QS is 64 and the length of TV is also 64.
To find the lengths of TV and QS, we'll set up an equation based on the given information and solve for w.
Given:
△QRS ≅ △TUV
QS = 4w + 16
TV = 6w - 8
To solve for w, we equate the corresponding sides of the triangles:
QS = TU
4w + 16 = 6w - 8
To isolate w, let's rearrange the equation:
4w - 6w = -8 - 16
-2w = -24
Divide both sides of the equation by -2:
w = (-24)/(-2)
w = 12
Now that we have the value of w, we can find the length of TV and QS by substituting w back into the given equations:
For QS:
QS = 4w + 16
QS = 4(12) + 16
QS = 48 + 16
QS = 64
For TV:
TV = 6w - 8
TV = 6(12) - 8
TV = 72 - 8
TV = 64
Therefore, the length of TV is 64 and the length of QS is also 64.
To find the length of TV and QS, we use the fact that corresponding sides of congruent triangles are equal in length.
Given: △QRS ≅ △TUV
We have:
QS = 4w + 16
TV = 6w - 8
Step 1: Set up an equation for the congruent sides.
Since △QRS ≅ △TUV, the corresponding sides QR and TU are equal in length.
QR = TU
Step 2: Set up an equation using the given side lengths.
We have:
QR = QS
TU = TV
So QR = QS and TU = TV.
Step 3: Substitute the given expressions for QS and TV into the equation.
Since QR = QS and TU = TV, we can substitute the given expressions into the equation.
QS = 4w + 16
TV = 6w - 8
So QR = 4w + 16 and TU = 6w - 8.
Step 4: Set the two expressions equal to each other.
Since QR = TU, we can set the two expressions equal to each other.
4w + 16 = 6w - 8
Step 5: Solve the equation.
To solve the equation, we need to isolate the variable w on one side.
Move the variable term to one side:
4w - 6w = -8 - 16
Combine like terms:
-2w = -24
Divide by -2 to solve for w:
w = (-24) / (-2)
w = 12
Step 6: Substitute the value of w back into the expressions for QS and TV.
QS = 4w + 16
TV = 6w - 8
Substituting w = 12:
QS = 4(12) + 16
TV = 6(12) - 8
Simplifying:
QS = 48 + 16
TV = 72 - 8
QS = 64
TV = 64
Therefore, the length of QS is 64 and the length of TV is also 64.