Aquilt maker is creating a design of a sailboat. she needs exactly the same amount of fabric for the sail as she needs for the body of the boat if the length of the bottom of the sail is equal to the short base of the boat what is the length of the long base of the trapezoid
a. 5
b. 10
c. 15
d. 25

The shape of sail is triangle
The shape of the boat is trapezoid
Fabric needed for sail = fabric needed for boat
which mean ;
                      the area of triangle = the area of trapezoid

the area of triangle = 0.5 * base * height
base = bottom sail = 10 and height = 10
∴  the area of triangle = 0.5 * 10 * 10 = 50 ⇒⇒⇒⇒⇒(1)

the area of trapezoid = 0.5 * (b₁ +b₂) * h
b₁ = long base
b₂ = short base = 10 cm.
h = height = 4 cm.
∴ the area of trapezoid = 0.5 (b₁ + 10 ) * 4 ⇒⇒⇒⇒ (2)

Equating (1) and (2)
∴ 0.5 (b₁ + 10 ) * 4 = 50
    b₁ + 10 = 25
    b₁  = 15

∴ The length of the long base of the trapezoid = 15 cm.

The correct answer is option (C)

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