the triangle and the trapezoid have the same base area. Base b2 is twice the area the length of b1. What are the lengths of the bases of the trapezoid?

b₁ = 7 cm, b₂ = 14 cm

Step-by-step explanation:

The area (A) of the triangle is calculated as

A = bh ( b is the base and h the height )

Here b = 21 and h = 6, then

A = 0.5 × 21 × 6 = 63 cm²

The area (A) of a trapezoid is calculated as

A = h (b₁ + b₂ )

Here A = 63 ( same as triangle ), h = 6 and b₂ = 2b₁ , then

0.5 × 6 × (b₁ + 2b₁ ) = 63

3 × 3b₁ = 63

9b₁ = 63 ( divide both sides by 9 )

b₁ = 7

and b₂ = 2 × 7 = 14

The bases of the trapezoid are 7 cm and 14 cm

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step-by-step explanation:

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