Mr Shen wished to enter the orange kite competition with an innovative kite of his own desgin. He did tests that showed an irregular quadrilateral design was best. The longest side (A) was twice the length of the shortest side (C). Side B was one and one-half times the shortest side (C). Side D needed to be 4" (4 inches) longer then side C. If the competition required that the perimeter of your kite must be 81", what were the dimensions of Mr. Shen's Kite?
Side C --- x
side A --- 2x
side B ----1.5x
side D ---- x+4
x + 2x + 1.5x + x+4 = 81
5.5x = 77
x = 14
plug in 14 into each of my definitions to find the lengths
I got the answers for A and B but how do I do that for C and D?
L A=28
Length B=21
I got those answers can you help me on the other 2?
To determine the dimensions of Mr. Shen's kite, we can use the information given and a system of equations to solve for the lengths of the kite's sides.
Let's assign variables to the lengths of the sides:
A: length of the longest side
B: length of side B
C: length of the shortest side
D: length of side D
Based on the information given, we can establish the following relationships:
1. A = 2C
2. B = 1.5C
3. D = C + 4
Now we can set up the equation based on the perimeter requirement of 81":
Perimeter = A + B + C + D
Substituting the values from the given relationships, we have:
81 = 2C + 1.5C + C + (C + 4)
Combining like terms, we get:
81 = 5.5C + 4
Subtracting 4 from both sides:
77 = 5.5C
Dividing both sides by 5.5:
C = 14
Now we can substitute the value of C back into the equations to find the lengths of the other sides:
A = 2C = 2 * 14 = 28
B = 1.5C = 1.5 * 14 = 21
D = C + 4 = 14 + 4 = 18
Therefore, the dimensions of Mr. Shen's kite are:
Side A: 28"
Side B: 21"
Side C: 14"
Side D: 18"