Question

the area of a Trapezium is 210 centimetre square and its height is 14 cm if one of the parallel sides is double that of the Other find the two parallel sides

Answer 1

hope you find it useful!!!

Answer 2

Answer:

The two parallel sides are of measure 10 cm and 20 cm respectively.

Step-by-step explanation:

$\text{Height of trapezium = 14 cm}\\\\\text{One parallel side is double to that of other parallel side.}\\\\\text{So, Let one parallel side be x cm.}\\\\\text{Then, the other parallel side will be 2x cm.}\\\\\therefore \: \text{We have the two parallel sides as x cm and 2x cm, and, the height as 14 cm}\\\\\text{Sum of parallel sides = x + 2x = 3x cm}\\\\\text{Then, area of trapezium = } \dfrac{1}{2}(\text{Sum of parallel sides})(\text{Height})$

$\text{Or, Area of trapezium = } \dfrac{1}{2}(3x)(14) = 7 \times 3x\\\\\\= \boxed{\boxed{\bold{21x \: cm^2}}}\\\\\\\text{But, given area of trapezium = 210 cm}^2\\\\\therefore \: \text{According to question,}\\\\\text{Area of trapezium = 21x cm ^2 = 210 cm ^2 }\\\\\text{Or, } 21x = 210\\\\\text{Or, } x = \dfrac{210}{21}\\\\\\\text{Or, } x = \boxed{\boxed{\bold{10}}}\\\\\text{The two parallel sides of the trapezium were found to be x and 2x cm.}$

$\large \underline{\boxed{\boxed{\bold{\therefore \: \: \text{The two sides are x = \boxed{10 \: cm} } \: \text{And, 2x = 2 \times 10 = \boxed{20 \: cm} .}}}}}$

$\text{We can also prove the answer.}\\\\\text{To do so, we should find the area of the trapezium again,}\\\text{taking the two parallel sides as 10 and 20 cm, and height, the same,}\\\text{i.e, 14 cm.}\\\\\text{Area of trapezium = } \dfrac{1}{2}(\text{Sum of parallel sides})(\text{Height})\\\\\\= \dfrac{1}{2}(10+20)(14)\\\\\\= 7 \times 30\\\\= \boxed{\boxed{\bold{210 \: cm^2}}}\\\\= \text{Given area of trapezium.}\\\\\textbf{Thus, the answer is correct.}$