Question

A new queen size bed sheet

Answer 1

Answer:

a) The dimensions of the sheet after washing are 205.8 cm and 235.2 cm

b) The percent decrease in the area of the sheet is 3.96%

Step-by-step explanation:

Let us solve the question

a)

∵ A new queen size bed sheet measures 210 cm by 240 cm.

∴ Length = 210 cm and width = 240 cm

∵ The length and width each shrinks by 2%

→ If the length is 100% and the width is 100%, they shrink by 2% each,

   then the new length is 98% of the original length and the new width

   is 98% of the original width

∴ The new length = 210 × 98% = 210 × $\frac{98}{100}$ = 210 × 0.98

∴ The new length = 205.8 cm

∴ The new width = 240 × 98% = 240 × $\frac{98}{100}$ = 240 × 0.98

∴ The new length = 235.2 cm

∴ The dimensions of the sheet after washing are 205.8 cm and 235.2 cm

b)

∵ The area of the rectangle = length × width

∴ The area of the original sheet = 210 × 240 = 50400 cm²

∴ The area of the sheet after washing = 205.8 × 235.2 = 48404.16 cm²

→ Percent of decrease = (decrease ÷ original) × 100%

∵ The decrease in area = 50400 - 48404.16 = 1995.84

∵ The original area = 50400

∴ The percent decrease = (1995.84 ÷ 50400) × 100%

∴ The percent decrease = 3.96%

∴ The percent decrease in the area of the sheet is 3.96%