You are helping some friends assemble a kite. They want to add a ribbon around the outside of the kite using the lengths indicat
ed in the diagram. The lengths given in the diagram are in inches.
How many inches of ribbon do you need to go the entire way around the kite?
Answer in a complete sentence. Provide supporting work in your solution.
How many inches of ribbon do you need to go the entire way around the kite?
Answer in a complete sentence. Provide supporting work in your solution.
2 answers:
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Answer: unit and 18 unit
Step-by-step explanation:
Let ABCD is a trapezoid where AB and CD are the bases. ( In which AB is greatest base which shown in below figure)
AD and BC are the legs of the trapezoid ABCD.
Now, we have ( According to the question ),
AB = 18 unit, BC = 7 unit, AD = 3 unit and DC = 11 unit.
Here the leg AD extends from point D.
Similarly leg BC extends from point C.
Let they meet at point P ( shown in below diagram)
Since In triangles PAB and PDC,
∠PDC ≅ ∠PAB ( because DC ║ AB )
And, ∠ PAB ≅ ∠ PBA
∠DPC ≅ ∠ APB ( reflexive)
Therefore, By AAA similarity postulate,
Thus, By the definition of similarity,
( because PA = PD+DA)
⇒ 18 PD = 11 PD +33
⇒7PD = 33
⇒ PD = 33/7
Again by the definition of similarity,
( because PB = PC + CB)
⇒ 18 PC = 11 PD +77
⇒7PC = 77
⇒ PC = 11
Thus, PA = PD+DA = 33/7 + 3 =
And, PB = PC + CB = 11 + 7 = 18
