Question

The area of the trapezium is 480m2 the distance between two parallel sides is 15m.The longer parallel side is longer than the other by 44m,find the length of the other parallel side.

Answer 1

Define x:

Let the length of the shorter parallel line be x.

The other parallel line will be x + 44.

Solve x:

Area of trapezium = 1/2 ( a + b ) (h)

480 = 1/2 ( x + x + 44) (15)

480 = 1/2 (2x + 44) (15)

480 = 15x + 330

15x = 150

x = 10

Find the length of the 2 parallel sides:

one side = x  = 10 m

the other side = x + 44 = 10 + 44 = 54 m

Answer: The lengths are 10 m and 54 m

Answer 2

Hellol

$\star \: \sf Height = 15\:m$

Let the length of shorter parallel line be $\bf{x}$
and Length of greater parallel line be $\bf{x+44}$

Then,

$\sf Area \:of\:Trapezium = 480\:m^{2} \\ \\ \implies \dfrac{1}{2}(\sf Sum\:of\:parallel \:sides) \times \sf Height = 480 \\ \\ \implies \dfrac{1}{2}(\sf x+x+44)\times 15 = 480 \\ \\ \implies \dfrac{1}{2}(\sf 2x+44)\times 15 = 480 \\ \\ \implies \sf 15x + 330 = 480 \\ \\ \implies \sf 15x = 480-330 \\ \\ \implies \sf x = \dfrac{150}{15} \implies \boxed{\red{\sf x = 10}}$

Hence,

• Length of $\underline{\sf shorter}$ parallel line = x = $\blue{\bf{10\:m}}$
• Length of $\underline{\sf greater}$ parallel line = x + 44 = $\blue{\bf{54\:m}}$

Cheers!