Trapezoid JKLM has an area of 54. If RC = 6 feet and ML = 8 feet, find JK.
We do not see the figure, so do not know if JK is parallel to LM, or JM is parallel to KL.
Also, we do not know where R and C are situated. I assume RC represents the height of the trapezoid, but cannot be sure.
To find the length of side JK in Trapezoid JKLM, we can use the formula for the area of a trapezoid. The formula is:
Area = (1/2) * (Sum of lengths of parallel sides) * (Height)
Given that the area of the trapezoid is 54 and the lengths of sides RC and ML are 6 feet and 8 feet respectively, we can substitute these values into the formula to solve for JK.
54 = (1/2) * (6 + JK) * 8
Now, let's solve the equation step by step:
Step 1: Distribute the fraction (1/2) into the parentheses:
54 = (3 + JK/2) * 8
Step 2: Simplify the equation further by distributing 8 into the parentheses:
54 = 24 + 4JK
Step 3: Subtract 24 from both sides of the equation to isolate 4JK:
54 - 24 = 24 - 24 + 4JK
30 = 4JK
Step 4: Divide both sides of the equation by 4 to find JK:
JK = 30/4
JK = 7.5
So, the length of side JK is 7.5 feet.