Question

ABCD is a rectangle.

EFGH is a trapezium.


F


x-3


E


A


Зr +4


B


5x


4x


5x


G


с


H


D


7x-3


The perimeters of these two shapes are the same.


All measurements are in centimetres.


(i) Work out the value of x.

Answer 1

The problem presented seems to require finding the value of x by equating the perimeters of a rectangle and a trapezium. However, there's insufficient information provided in the question as it includes an undefined value 'r', preventing us from solving for x without more context or additional equations relating r and x.

Step-by-step explanation:

The question involves finding the value of x when the perimeters of a rectangle and a trapezium are given to be the same. To begin solving the problem, let's sum up the sides of the rectangle ABCD, knowing that opposite sides of a rectangle are equal:

• AB + BC + CD + DA = 2(AB) + 2(BC)
• (3r + 4) + (5x) + (3r + 4) + (5x) = 2(3r + 4) + 2(5x)
• 6r + 8 + 10x

Now, let's find the sum of the sides of the trapezium EFGH:

• EF + FG + GH + HE
• (x - 3) + (4x) + (7x - 3) + (5x)
• x - 3 + 4x + 7x - 3 + 5x
• 17x - 6

Since the perimeters are the same, we can set them equal to each other:

Answer 2

The value of x obtained from the definition of the perimeter of a rectangle and the perimeter of a trapezoid is x = 3.5

The steps to find the value of x are as follows;

The perimeter of the rectangle is; 2 × ((3·x + 4) + 4·x) = 14·x + 8

The perimeter of the trapezoid is; 2 × 5·x + (x - 3) + (7·x - 3) = 18·x - 6

The perimeter of the rectangle and the perimeter of the trapezoid are the same, therefore;

14·x + 8 = 18·x - 6

18·x - 14·x = 8 + 6

4·x = 14

x = 14/4

x = 3.5

The value of x is 3.5 units

Please find attached the possible diagrams in the question obtained from a similar question found through search