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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 × = 210 × 0.98
∴ The new length = 205.8 cm
∴ The new width = 240 × 98% = 240 × = 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%