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# This rectangular prism....

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This rectangular prism is intersected by a plane that contains points D, E, K, and L.

What is the perimeter of the cross section?

Enter your answer in the box. Round only your final answer to the nearest tenth.

May 24, 2018

#1
+8579
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The perimeter of the cross section is the perimeter of rectangle DEKL.

perimeter of DEKL  =  DE + EK + KL + LD

(where  DE ,  EK ,  KL , and  LD  are in meters)

KL  =  12     and     DE  =  12

To find the length of EK, look at right triangle EJK.

By the Pythagorean theorem,

EJ2  +  JK2   =   EK2

Plug in  5  for  EJ  and  4  for  JK .

52   +   42   =    EK2
Simplify the left side of the equation.

25  +  16   =   EK2

41   =   EK2

Take the positive square root of both sides.

√41  =  EK

So.....

EK  =  √41     and     LD  =  √41

perimeter of DEKL  =  DE + EK + KL + LD

Plug in the values of  DE ,  EK ,  KL , and  LD .

perimeter of DEKL  =  12 + √41 + 12 + √41

Combine like terms.

perimeter of DEKL  =  24 + 2√41

May 24, 2018

#1
+8579
+2

The perimeter of the cross section is the perimeter of rectangle DEKL.

perimeter of DEKL  =  DE + EK + KL + LD

(where  DE ,  EK ,  KL , and  LD  are in meters)

KL  =  12     and     DE  =  12

To find the length of EK, look at right triangle EJK.

By the Pythagorean theorem,

EJ2  +  JK2   =   EK2

Plug in  5  for  EJ  and  4  for  JK .

52   +   42   =    EK2
Simplify the left side of the equation.

25  +  16   =   EK2

41   =   EK2

Take the positive square root of both sides.

√41  =  EK

So.....

EK  =  √41     and     LD  =  √41

perimeter of DEKL  =  DE + EK + KL + LD

Plug in the values of  DE ,  EK ,  KL , and  LD .

perimeter of DEKL  =  12 + √41 + 12 + √41

Combine like terms.

perimeter of DEKL  =  24 + 2√41

hectictar May 24, 2018