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

Answer:

a. Area = 1.94m²

b. Area = (p² + 0.5)m²

c. Height = 1.5m

Step-by-step 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

$\sqrt{2.25} = \sqrt{H^2}$

$\sqrt{2.25} = H$

$1.5 = H$

$H = 1.5$

Hence, the height is 1.5m