P-1 Linear Equations in Two Variables — Maths STD 10 — Question

In the adjoining fig. ⬜ABCD is a trapezium AB||CD and its area is 33 cm². From the information given in the figure find the lengths of all sides of the ⬜ABCD. Fill in the empty boxes to get the solution.

⬜ $\square ABCD$ is a trapezium. $AB \| CD$
Area of trapezium
$=\frac{1}{2} \times($ Sum of parallel sides $) \times$ Height
$\therefore \quad A (⬜ABCD )=\frac{1}{2} \times( AB + CD ) \times$⬜
$\therefore \quad 33=\frac{1}{2}(x+2 x+1) \times$⬜
∴ ⬜$=(3 x+1) \times$ ⬜
$\therefore \quad 66=3 x^2-12 x+x-4$
$\therefore \quad 3 x^2$ - ⬜ - ⬜ = 0
$\therefore \quad 3 x^2-21 x+10 x-70=0$
$\therefore \quad 3 x(x-7)+10(x-7)=0$
$\therefore \quad(3 x+10)(x-7)=0$
By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
$\therefore \quad(3 x+10)=0$ or ⬜ = 0
$\therefore \quad x=\frac{-10}{3}$ or $x=$ ⬜
But, length is never nagative.
∴ $x \neq \frac{-10}{3}$
∴ x = ⬜
AB = ⬜
CD = ⬜
AD = BC = ⬜