The perimeter of isosceles trapezoid KLMN is 3√2 + 2√5 units ⇒ 3rd answer
Step-by-step explanation:
The isosceles trapezoid has
The formula of the slope of a line whose endpoints are [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
∵ KLMN is an isosceles trapezoid, whose vertices are:
K (-2 , -4) , L (-4 , -2) , M (-2 , -1) , N (-1 , -2)
- Let us find the slopes of its sides to find the parallel sides
∵ [tex]m_{KL}=\frac{-2--4}{-4--2}=\frac{-2+4}{-4+2}=\frac{2}{-2}=-1[/tex]
∵ [tex]m_{LM}=\frac{-1--2}{-2--4}=\frac{-1+2}{-2+4}=\frac{1}{2}=0.5[/tex]
∵ [tex]m_{MN}=\frac{-2--1}{-1--2}=\frac{-2+1}{-1+2}=\frac{-1}{1}=-1[/tex]
∵ [tex]m_{NK}=\frac{-4--2}{-2--1}=\frac{-4+2}{-2+1}=\frac{-2}{-1}=2[/tex]
∴ The slope of KL = the slope of MN
∴ KL // MN ⇒ parallel bases
∴ The slope of LM not equal the slope of KN
∴ LM not parallel to KN
∴ LM = KN
∵ The perimeter of the isosceles trapezoid equal the sum of the
parallel bases and the equal sides
∴ The perimeter = KL + LM + MN + NK
∵ KL = 2√2 units , LM = √5 units , MN = √2 units
∵ LM = KN
∴ KN = √5 units
∴ The perimeter = 2√2 + √5 + √2 + √5
∴ The perimeter = 3√2 + 2√5 units
The perimeter of isosceles trapezoid KLMN is 3√2 + 2√5 units
Learn more:
You can learn more about trapezoid in brainly.com/question/7287774
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Answer:
C) [tex]2\sqrt{2} + 2\sqrt{5}[/tex] units
Step-by-step explanation:
it's the third option, i just took the test
perimeter = all the sides lengths added together
