Question

Hey guys please solve this questions
1】The parallel sides of a Trapezium are in the ratio 2 : 3 .If its area is 750 CM square and height 15 cm find the length of the parallel sides .
2】the area of a Trapezium is 270 CM square and its height is 12 CM. if one of the parallel sides is longer than the other by 5 cm, find the length of two parallel sides.

Please help!!

Answer 1

1) since, height of a trapezium = 15cm

let x be the ratio between the parallel sides , such that :

one parallel side = 2x

and, other parallel side = 3x

we know that,

area of a trapezium = $\frac{1}{2}$ × (sum of parallel sides) × height

=> 750 cm² = $\frac{1}{2}$ × (2x + 3x) × 15

let us take 15 to other side, so that if it is multiplying, so after going to other side it will divide,

=> $\frac{750}{15}$ = $\frac{1}{2}$ × 5x

=> 50 = $\frac{1}{2}$ × 5x

take $\frac{1}{2}$ to other side,

=> 50 × 2 = 5x

=> 100 = 5x

take 5 to other side,

=> x = $\frac{100}{5}$

=> x = 20

thus, one parallel side = 2x = 2×20 = 40 cm
and, other parallel side = 3x = 3×20 = 60 cm (answer)

2) since, height of a trapezium = 12cm

let x be the other parallel side,

so, one parallel side = ( x + 5 ) cm

and, area of trapezium = $\frac{1}{2}$ × (sum of parallel sides) × height

=> 270 cm² = $\frac{1}{\cancel{2}}$ × (x + x + 5) × $\cancel{12}$

=> 270 = (2x + 5) × 6

take 6 to other side,

=> $\frac{270}{6}$ = 2x + 5

=> 45 = 2x + 5

take 5 to other side,

=> 45 - 5 = 2x

=> 40 = 2x

take 2 to other side,

=> x = $\frac{40}{2}$

=> x = 20

thus,

other parallel side = x = 20 cm

and, one parallel side = x + 5 = 20 + 5 = 25cm (answer)