Question

quadrilateral tuvw is a rectangle, tv = 5s + 96, and uw = 19s + 40. what is uw?

Explanation:

Step1: Use the property of rectangle diagonals

In a rectangle, the diagonals are equal. So \( TV = UW \).

$$5s + 96=19s + 40$$

Step2: Solve the equation for \(s\)

Subtract \(5s\) from both sides:

$$96 = 14s+40$$

Subtract \(40\) from both sides:

$$56 = 14s$$

Divide both sides by \(14\):

$$s=\frac{56}{14}=4$$

Step3: Find the value of \(UW\)

Substitute \(s = 4\) into the formula for \(UW\) (\(UW=19s + 40\)):

$$UW=19\times4+40$$

$$UW = 76+40$$

$$UW=116$$

Answer:

\(116\)