Question

The dimensions of a photo

frame are identified in the
image below.
a)
Determine a simplified
expression for the area
of the frame. [2 marks]
b) Calculate the area if
x=2cm. [1 marks]
8x
-10cm
(10x + 4 - 5) cm
(10.x
4) cm

Answer 1

The area of the photo frame is represented by
`\(80x^2 - 68x - 90\)`. When
`\(x = 2\)` cm, the calculated area is
`\(94 \, \text{cm}^2\)`.

a) To find the area of the photo frame, we need to compute the product of its length and width. The length of the frame is represented by the expression (10x + 4 - 5) cm, and the width is represented by (8x - 10) cm. The area ((A)) can be expressed as:

`\[ A = (10x + 4 - 5) \cdot (8x - 10) \]`

Now, distribute and simplify:

`\[ A = (10x + 4 - 5)(8x - 10) \]`

`\[ A = 80x^2 - 100x + 32x - 40 - 50 \]`

`\[ A = 80x^2 - 68x - 90 \]`

The simplified expression for the area of the frame is
`\(80x^2 - 68x - 90\)`.

b) To calculate the area when (x = 2) cm, substitute (x = 2) into the simplified expression:

`\[ A = 80(2)^2 - 68(2) - 90 \]`

`\[ A = 320 - 136 - 90 \]`

`\[ A = 94 \, \text{cm}^2 \]`

Therefore, when (x = 2) cm, the area of the photo frame is
`\(94 \, \text{cm}^2\)`.