Question

one of the parallel sides of a trapezium twice the other.if the distance between themis 5 cm and the area is 45 cm square ,find the length of the parallel side​

Answer 1

Given:

A trapezium with

• First parallel side = x cm
• Second parallel side twice than first parallel side = 2x cm
• Distance between them = 5 cm
• Area = 45 cm²

To Find:

Length of first and second parallel sides i.e., x and 2x.

How To Find?

To find the length of first and second parallel sides we will use the formula $\sf{Area\:of\:trapezium=\dfrac{1}{2}\times height\times(sum\:of\:parallel\:sides)}$ and substitute the values.

Solution:

Using the formula,

⇒ $\sf{Area\:of\:trapezium=\dfrac{1}{2}\times height\times(sum\:of\:parallel\:sides)}$

Substitute the values,

⇒ $\sf{45\:cm^{2} =\dfrac{1}{2}\times5\:cm\times(x+2x)}$

Solve the brackets in RHS,

⇒ $\sf{45\:cm^2=\dfrac{1}{2}\times5\:cm\times3x}$

Take 2 to LHS,

⇒ $\sf{45\times2=5\times3x}$

Multiply 45 by 2 in LHS and 5 by 3x in RHS,

⇒ $\sf{90=15x}$

Take 15 to LHS,

⇒ $\sf{\dfrac{90}{15}=x}$

Divide 90 by 15,

⇒ $\sf{6\:cm=x}$

∴ Therefore,

• First parallel side = x cm = 6 cm
• Second parallel side = 2x cm = 2(6) cm = 12 cm