Answer :
Answer:
4 m and 8 m
Step-by-step explanation:
To determine how long the bases of the trapezoid are, we can use the area of a trapezoid formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Area of a trapezoid}}\\\\A=\dfrac{h(b_1+b_2)}{2}\\\\\textsf{where:}\\ \phantom{ww}\bullet\;\textsf{$A$ is the area.}\\ \phantom{ww}\bullet\;\textsf{$b_1$ and $b_2$ are the bases (parallel sides).}\\\phantom{ww}\bullet\;\textsf{$h$ is the height (perpendicular to the bases).}\end{array}}[/tex]
In this case, one of the bases is twice as long as the other. So, if we let one base equal x, then the other base is 2x.
So, the values to substitute into the area equation are:
- A = 36 m²
- h = 6 m
- b₁ = x
- b₂ = 2x
Substitute these values into the equation and solve for x:
[tex]36=\dfrac{6(x+2x)}{2}\\\\\\36=\dfrac{6(3x)}{2}\\\\\\36=\dfrac{18x}{2}\\\\\\72=18x\\\\\\x=\dfrac{72}{18}\\\\\\x=4[/tex]
Therefore, the bases of the trapezoid are 4 m and 8 m long.
