+309 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.
+9481 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
+9481 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
