Question

area of a trapezium is 351 sq.cm, its parallel side are in ratio 5 : 8 and their difference is 18 cm. Find the sum of other two equal sides of trapezium if length of its diagonals are equal

Answer 1

Answer:

1/2 *(a+b)h

a/b=5/4

b-a =18 ................ 1

b = 8a /5

b-a =18

8a /5 -a = 18

3a /5 =18

a = 18*5/3

a = 30 cm

b = 8a /5

= 8*30/5

= 48 cm

Area of the trapizum=1/2*(a+b)h

153 =1/2*(30+48) h

h = 153*2/78

= 3 cm

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Answer 2

Given:

$\bold {\green{\texttt{Area of trapezium \bf = 351cm^2 }}}$

$\bold {\green{\texttt{Parallel sides are in ratio \bf 5 : 8 }}} \\ \therefore \red{\textsf{Let the sides be \bf 5x and \bf 8x }}$

$\bold{\green{\texttt{The difference of the parallel sides is = \sf 18cm }}} \\ \therefore \sf 8x - 5x = 18cm \\ \implies 3x = 18cm \\ \implies x = \frac{18}{3} \\ \implies \bf x = 6 \\ \therefore {\blue{\texttt{So, Now :- }}} \\ \bf \implies 5x = 5 \times 6 = \pink{35cm} \\ \bf \implies 8x = 8 \times 6 = \pink{48 cm} \\ \therefore \bold {\pink{\texttt{ The parallel sides of the trapezium are \bf 35 cm and \bf 48cm }}}$

$\bold{\green{\texttt{The length of its diagonal is equal}}}$

To find : the height of trapezium.

$\boxed{\red{\texttt{Formula for area of trapezium = \sf \frac{a + b}{2}h }}}$

Also, area = $\sf \bold{351cm^2}$

a = 35cm

b = 48cm

Putting the values,

$\therefore \sf 351cm^2 = \frac{35 + 48}{2} h \\ \sf \implies 351cm^2 = \frac{83}{2}h \\ \sf \implies 351cm^2 = 41.5 \times h \\ \sf \implies h = \frac{351cm^2}{41.5} \\ \sf \implies \bold{\red{h = 8.5}}$

$\pink{\texttt{The height of the trapezium is 8.5 cm}}$