A property of rectangles is that opposite sides are congruent. In this case, since QT and RS are opposite sides, they are equal to each other. With this knowledge, you can form the equation $50=4x+8$ to solve for x.

Firstly, subtract both sides by 8: $42=4x$

Next, divide both sides by 4 and your answer will be $10.5=x$ , or the third option.

6 0

3 years ago

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Gennadij [26K]

Answer:

x = 4

Step-by-step explanation:

Using the sine ratio on right triangle KJL

and the exact value sin30° = $\frac{1}{2}$

sin30° = $\frac{opposite}{hypotenuse}$ = $\frac{JL}{KL}$ = $\frac{JL}{8\sqrt{2} }$ = $\frac{1}{2}$ ( cross- multiply )

2JL = 8 $\sqrt{2}$ ( divide both sides by 2 )

JL = 4 $\sqrt{2}$

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Using the sine ratio in right triangle JLM

and the exact value sin45° = $\frac{1}{\sqrt{2} }$

sin45° = $\frac{opposite}{hypotenude}$ = $\frac{LM}{JL}$ = $\frac{x}{4\sqrt{2} }$ = $\frac{1}{\sqrt{2} }$ ( cross- multiply )

x × $\sqrt{2}$ = 4 $\sqrt{2}$ ( divide both sides by $\sqrt{2}$

x = 4

8 0

3 years ago