Question

y 2x 3x y The diagram shows a trapezium. All the lengths are in centimetres. The perimeter of the trapezium is P cm. Find a formula, in terms of x and y, for P. Give your answer in its simplest form.​

Answer 1

To find:-

• The perimeter of the trapezium.

Answer :-

Perimeter: Perimeter is simply the sum of all the side lengths of a figure. Here it is a trapezium so the perimeter would be the sum of all the four sides.

According to the given question , the expressions of the side lengths are , 2x , y , 3x and y .

So the perimeter would be the sum of these four expressions as ,

P = 2x + y + 3x + y

Group like terms ,

P = 2x + 3x + y + y

Add like terms ,

P = 5x + 2y

Also the unit here is centimetres, so the perimeter would be (5x + 2y)cm .

Therefore, the required formula for perimeter is ,

P = (5x + 2y) cm

and we are done!

Answer 2

`P=(5x+2y)\; \sf cm`

Explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside. Therefore, the perimeter of a trapezium is the sum of its side lengths.

From inspection of the given diagram, the side lengths of the trapezium are:

• 2x cm
• y cm
• 3x cm
• y cm

Therefore, the formula for its perimeter, P, in terms of x and y is:

`\implies P=2x+y+3x+y`

Simplify by collecting like terms:

`\begin{aligned}\implies P&=2x+y+3x+y\\&=2x+3x+y+y\\&=5x+2y\\\end{aligned}`

Therefore, the formula, in terms of x and y, for P in its simplest form is:

`P=(5x+2y)\; \sf cm`