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Chapter 1 - Tools of Geometry - 1-8 Perimeter, Circumference, and Area - Practice and Problem-Solving Exercises - Page 64: 7
Answer
Work Step by Step
The perimeter $P$ of a polygon is the sum of the length of its sides. For rectangles in particular, the formula for perimeter is $P=2b+2h$. The figure shows a rectangle with a base of $7$ and a height of $4$. We plug these values into the formula and simplify: $$P=2(7)+2(4)$$$$P=14+8$$$$P=22\text{ in}$$
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Chapter 1 - Tools of Geometry - 1-3 Measuring Segments - Practice and Problem-Solving Exercises - Page 24: 19
Answer
Work Step by Step
If A is the midpoint of $\overline{XY}$, then $\overline{XA}=\overline{AY}$ (according to the definition of a midpoint). So, we can set up an equation using the values of $\overline{XA}$ and $\overline{AY}$ and setting them equal to each other. Our equation is $3x=5x-6$ Thus, we obtain: $$-2x=-6 \\ x=3$$ We now substitute 3 into the expressions. $XA=3x=3(3)=9$. $AY=5x-6=5(3)-6=15-6=9$ $XY=3x+5x-6=8x-6=8(3)-6=24-6=18$.
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