Question

If the width of the uniform shaded portion of x m; its area in terms of x is ______.

Options

• 320 m² – (16 – 2x)(20 – 2x) m²

• 320 m² – (16 – x)(20 – x) m²

• 320 m² – (16 – 2x)(20 – x) m²

• 320 m² – (16 – x)(20 – 2x) m²

Answer 1

If the width of the uniform shaded portion of x m; its area in terms of x is 320 m² – (16 – 2x)(20 – 2x) m².

Explanation:

Length of outer rectangle = 20 m

Breadth of outer rectangle = 16 m

∴ Area of outer rectangle

= Length × Breadth

= 20 × 16 m²

= 320 m²

Given width of shaded portion = x metre

∴ Length of inner rectangle = (20 – 2x) m

Breadth of inner rectangle = (16 – 2x) m

∴ Area of inner rectangle = (20 – 2x)(16 – 2x)

Thus, area of shaded portion = area of outer rectangle – area of inner rectangle

= 320 – (20 – 2x)(16 – 2x) m²