Answer:
<h2>The lengths of the bases of the trapezoid:</h2><h2>42/h cm and 84/h cm.</h2>Step-by-step explanation:
The formula of an area of a triangle:
<em>b</em><em> </em>- base
<em>h</em> - height
We have <em>b = 21cm, h = 6cm</em>.
Substitute:
The formula of an area of a trapezoid:
<em>b₁, b₂</em> - bases
<em>h</em><em> - </em>height
We have <em>b₁ = 2b₂</em>, therefore <em>b₁ + b₂ = 2b₂ + b₂ = 3b₂</em>.
The area of a triangle and the area of a trapezoid are the same.
Therefore
<em>multiply both sides by 2</em>
<em>divide both sides by 3</em>
<em>divide both sides by h</em>