Question

the difference between two parallel sides of a trapezium is 8 m. The perpendicular distance between them is 24 m. Find the length of the two parallel sides, if the area of the trapezium is 312 m².

Answer 1

Hey MATE!

We know that area of trapezium is:

$\frac{1}{2} \times (sum \: of \: parallel \: sides \: ) \times \: perpendicular \: distance \: between \: parallel \: sides$


Let the length of larger side be x m and that of shorter side be y m.

Therefore,

$\frac{1}{2} \times (x + y) \times 24 = 312$
$12 \: (x + y) = 312 \\ x + y = \frac{312}{12} \\ x + y = 26 - - - - - - equation \: 1.$
Now the difference of the 2 sides is given as :

x - y = 8--------equation 2

Add equations 1 and 2

x + y = 26

+ x - y = 8
----------------------
2x = 34

x = 17 m

Put value of x in 2.

17 - y = 8

17 - 8 = y

y = 11 m

THEREFORE THE PARALLEL SIDES OF TRAPEZIUM ARE :

X = 17 m

Y = 11 m

Hope it helps

Hakuna Matata :))