Question

the area of a trapezium is 144cm2.the length one of the parallel sides is 12cm and it's height is 15cm. find the length of other parallel side ​

Answer 1

Area = 144 sq.cm

one parallel side=12 cm

height = 15 cm

Let the other parallel side be b

ar. of trap. = half* (sum of parallel side)*height

144 sq.cm= 1/2*(12+b)*15

144/15 = 1/2*(12+b)

9.60=1/2*(12+b)

9.60/2=(12+b)

4.8=12+b

b= 12-4.8

7.2

Answer 2

$\begin{gathered}\frak{Given}\begin{cases}\sf{Area \ of \ the \ trapezium = 180 \ cm^2}\\\sf{Height \ of \ the \ trapezium = 12 \ cm}\\\sf{One \ || \ side \ is \ double \ the \ other \ side}\end{cases}\end{gathered}$

Let's consider that first side of the trapezium be x cm & second side be 2x cm.

$\begin{gathered}\\\end{gathered}$

By using Trapezium Formula,

$\star\ \boxed{\sf{\purple{Area_{(Trapezium)} = \frac{1}{2} \times (Sum \ of \ || \ sides) \times (Height)}}}⋆$

$\begin{gathered}\\\end{gathered}$

☯ Substituting the Given values

$\begin{gathered}:\implies\sf 180 = \dfrac{1}{2} \times (x + 2x) \times 12 \\\\\\:\implies\sf 180 = \dfrac{1}{\cancel{\: 2}} \times 3x \times \cancel{12} \\\\\\:\implies\sf 180 = 3x \times 6\\\\\\:\implies\sf 180 = 18x \\\\\\:\implies\sf x = \cancel\dfrac{180}{18}\\\\\\:\implies\boxed{\frak{\pink{\: x = 10 cm \: }}}\end{gathered}$

$\begin{gathered}\\\end{gathered}$

$\sf \red{ The \: Length \: of \: the || sides \: are :}$

$\tt{First \: side, x = 10 cm}$

$\tt{Second \: side, 2x = 20 cm}$