Question

You are making the kite shown at the right from five pairs of congruent panels. In parts (a)–(d) below, use the given information to find the side lengths of the kite’s panels. ABCD is a kite. EB = 15 in., BC = 25 in. The extended ratio XY: YZ : ZC is 3: 1: 4. EX is parallel to BC, EX is parallel to YF is parallel to GZ a. nBEX c. YFGZ b. XEFY d. nZGC

Answer 1

a. Triange BEX = 9 Inches

b. XEFY = 6 Inches

c. YFGZ = 2Inches

d. Triangle ZGC = 8 Inches

Step-by-step explanation:

Given that:

BC = 25 Inch

EB=15 Inch

(a)In Triangle BEX

EB is the Hypotenuse.

Using the idea of Pythagorean Triples (9,12,15), the other two legs of Triangle BEX will be 12 Inches and 9 Inches respectively.

From observation, BX is shorter than EX, therefore:

Side Length BX = 9 Inches.

BC=BX+XC

25=9+XC

XC=25-9

XC=16 Inches.

Given that the extended ratio:

`XY\colon YZ\colon ZC=3\colon1\colon4.`
`\begin{gathered} XY=(3)/(8)*16=6\text{ Inches} \\ YZ=(1)/(8)*16=2\text{ Inches} \\ ZC=(4)/(8)*16=8\text{ Inches} \end{gathered}`

Therefore, the side lengths of the given panels are:

• a. Triange BEX = 9 Inches

,

• b. XEFY = 6 Inches

,

• c. YFGZ = 2Inches

,

• d. Triangle ZGC = 8 Inches