Question

The area of trapezium is 850 sq. cm. One of the parallel sides is 64 cm and the perpendicular distance between the parallel sides is 17 cm. Find the length of other parallel side.

Answer 1

Area of trapezium =850 cm²
distance = height =17cm
first parallel side =64cm another
Area of trapezium =½*(sum of parallel side) h=850cm²
½(x+64cm)17cm =850cm²
x+64cm=850*2/17
x+64cm=100cm
x=100-64cm
x=36cm
another parallel side =36cm

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

★Area of the trapezium :-

= 850 cm²

★Length of 1st parallel side

(a) = 64 cm

(h) = 17 cm

★Assume the length of 2nd parallel side be n cm

★We know that :-

${\boxed{\sf\:{Area\;of\;Trapezium=\dfrac{1}{2}\times h\times(a+n)}}}$

$\tt{\rightarrow 850=\dfrac{1}{2}\times 17\times(64+n)}$

$\tt{\rightarrow 850=\dfrac{17}{2}\times (64+n)}$

$\tt{\rightarrow 850\times\dfrac{2}{17}=64+n}$

$\tt{\rightarrow\dfrac{1700}{17}=64+n}$

⇒ 100 = 64 + n

⇒ 100 - 64 = n

⇒ 36 = n

⇒ n = 36

★Hence :-

$\fbox{Length\:of\:the\:2nd\:parallel\:side\:is\:36cm}$