Question

A table cloth of length 50 cm and width 35 cm has a lace border of uniform width 2.5 cm. Find the area of the lace border.



Please give me the answer. Answer should be 400cm².​

Answer 1

Given : A table cloth of length 50 cm and width 35 cm has a lace border of uniform width 2.5 cm. Find the area of the lace border.

Solution : According to the question here we are given that the length of the table cloth is 50 cm, the width is 35 cm and has a lace border of width 2.5 cm

Let's get the area of lace border

Length = 50 cm

Width = 35 cm

Width (Lace Border) = 2.5 cm

Area of tablecloth = Length × Breadth

• Area = 50 cm × 35 cm

• Area = 1750 cm²

Henceforth, the area is tablecloth is 1750 cm²

Now, as we include lace so there should decrease in the length and width of cloth

Length₁ = 50 cm - 2.5 cm - 2.5 cm = 45 cm

Width₁ = 35 cm - 2.5 cm - 2.5 cm = 30 cm

• Area = Length₁ × Width₁

• Area = 45 cm × 30 cm

• Area = 1350 cm²

Henceforth, the area is tablecloth including lace is 1350 cm²

Therefore, area of lace border = 1750 cm² - 1350 cm² = 400 cm²

★ The area of lace border is 400 cm² ★

Answer 2

Given :

• Length of the Tablecloth = 50 cm
• Breadth of the Tablecloth = 35 cm
• Width of laceborder = 2.5 cm

$\\ {\underline{\rule{200pt}{3pt}}}$

To Find :

• Area of the lace border = ?

$\\ {\underline{\rule{200pt}{3pt}}}$

Solution :

Formula Used :

• Area of Rectangle :

$\large{\orange{\bigstar \: \: {\underbrace{\underline{\purple{\sf{ Area{\small_{(Rectangle)}} = Length \times Breadth }}}}}}}$

• Where :

Length = 50 cm

Breadth = 35 cm

$\\ \qquad{\rule{150pt}{1pt}}$

Calculating the Area of Bedsheet including Borders :

Here :

• ↠ Area = ?
• ↠ Length = 50 cm
• ↠ Breadth = 35 cm

Area of Tablecloth :

${\longmapsto{\qquad{\sf{ Area = Length \times Breadth }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Area = 50 \times 35 }}}} \\ \\ \ {\qquad{\sf{ Area \: of \: Bedsheet{\small_{(Including \: Borders )}} = {\blue{\sf{ 1750 \: cm² }}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

Calculating Area of Tablecloth without borders :

Here :

• Length' = 50 - 2.5 - 2.5 = 45 cm
• Breadth' = 35 - 2.5 - 2.5 = 30 cm
• Area' = ?

Area of Tablecloth :

${\longmapsto{\qquad{\sf{ Area' = Length' \times Breadth' }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Area' = 45 \times 30 }}}} \\ \\ \ {\qquad{\sf{ Area \: of \: Bedsheet{\small_{(Without \: Borders )}} = {\pink{\sf{ 1350 \: cm² }}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

Calculating the Area of Borders :

${\dashrightarrow{\qquad{\sf{ Area{\small_{(Borders)}} = Area - Area' }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ Area{\small_{(Borders)}} = 1750 - 1350 }}}} \\ \\ \ {\qquad{\textsf{ Area of the Borders = {\orange{\sf{ 400 \: cm² }}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

Therefore :

❝ Area of the Borders is 400 cm² . ❞

$\\ {\underline{\red{\rule{300pt}{9pt}}}}$