The diagram shows two rectangles, A and B - OCR - GCSE Maths - Question 4 - 2019 - Paper 1

Let the height of rectangle B be denoted as ( h ). Since the width of rectangle B is three times the height, it can be expressed as ( 3h ).

The area of rectangle B is given by:

$$\text{Area of B} = \text{width} \times \text{height} = 3h \times h = 3h^2$$

Since the area of rectangle A is equal to the area of rectangle B, we have:

$$300 = 3h^2$$

To find ( h ), we rearrange the equation:

$$3h^2 = 300$$

Dividing both sides by 3 gives:

$$h^2 = 100$$

Taking the square root of both sides results in:

$$h = 10 \text{ cm}$$

Now that we have the height of rectangle B, we can find the width:

$$\text{Width of B} = 3h = 3 \times 10 = 30 \text{ cm}$$

The perimeter of a rectangle is calculated using the formula:

$$\text{Perimeter} = 2 \times (\text{width} + \text{height})$$

Substituting the values for rectangle B:

$$\text{Perimeter} = 2 \times (30 + 10) = 2 \times 40 = 80 \text{ cm}$$

Therefore, the perimeter of rectangle B is 80 cm.