Question

To work out the area in m² of material required for a pair of curtains, a seamstress squares the height of the window in m and adds 0.5.

a) What area of material is required for a window of height 1.2meters?

b) What area of material is required for a window of height p meters?

c) if the area of material required is 2.75m²,what is the height of the window?​

Answer 1

a. Area = 1.94m²

b. Area = (p² + 0.5)m²

c. Height = 1.5m

Explanation:

Given

Let H represents Height and A represents Area

From the first and second statements, we have that:

`A = H^2 + 0.5`

a. Calculating Area When Height = 1.2

`A = H^2 + 0.5`

Substitute 1.2 for H

`A = 1.2^2 + 0.5`

`A = 1.44 + 0.5`

`A = 1.94`

Hence, the area is 1.94m²

b. Calculating Area When Height = p

`A = H^2 + 0.5`

Substitute p for H

`A = p^2 + 0.5`

Hence, the area is (p² + 0.5)m²

c. Calculating Height When Area = 2.75m²

`A = H^2 + 0.5`

Substitute 2.75 for A

`2.75 = H^2 + 0.5`

Subtract 0.5 from both sides

`2.75 - 0.5 = H^2 + 0.5 - 0.5`

`2.75 - 0.5 = H^2`

`2.25 = H^2`

Take Square Root of both sides

`√(2.25) = √(H^2)`

`√(2.25) = H`

`1.5 = H`

`H = 1.5`

Hence, the height is 1.5m