What is the perimeter of rectangle JKLM?32 units44 units56 units64 units

Accepted Solution

Answer: Third option. Step-by-step explanation: The missing figure is attached. The perimeter of a rectangle can be calculated with: [tex]P=2l+2w[/tex] Where "l" is the length and "w" is the width. We can see that the width of this rectangle is: [tex]w=12\ units[/tex] So, we need to find the lenght. Let be P the point  of intersection of the diagonals. The diagonals of a rectangle are equal. Since: [tex]JM=12\\MO=10[/tex] We know that, by definition: [tex]JP=LP=MP=KP[/tex] Then, we can find the lenght of the rectangle by using the Pythagorean Theorem: [tex]MK^2=KL^2+LM^2[/tex] We can identify that: [tex]MK=10\ units+10\ units=20\ units\\KL=12\ units[/tex] Then, subsituting values and solving for "LM", we get: [tex]20^2=LM^2+12^2\\\\LM=\sqrt{20^2-12^2}\\\\LM=16\ units[/tex] Substituting values into the formula for calculate the perimeter, we get: [tex]P=2(16}\ units)+2(12\ units)=56\ units[/tex]