Question

The two parallel sides and distance between them are in the ratio 3:4:2. If the area of the trapezium is 175cm². Find its height

Answer 1

let the two parallel sides of the trapezium be 3x and 4x and height be 2x.
area of the trapezium = 175cm²

therefore 1/2×h(b1+b2) = 175cm²
=> 1/2×2x(3x+4x) = 175cm²
=> x×7x = 175cm²
=> 7x² = 175cm²
=> x² = 175/7
=> x² = 25
=> x = √25
=> x = 5

hence parallel sides are 3x and 4x.
→ 3x = 3×5
= 15cm

→ 4x = 4×5
= 20cm
→ height of the trapezium = 2x
= 2×5
= 10cm

VERIFICATION:-

area of the trapezium = 1/2×h(b1+b2)
= 1/2×10(15+20)
= 5×35
= 175cm²
hence verified
hope this helps u..!