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

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)