Question

Gita was feeling hungry, and so she thought to eat something. She looked into the refrigerator and found some bread and cheese. She decided to make cheese sandwiches. She cut the piece of bread diagonally and found that it forms a right-angled triangle with sides containing the right angle are 4 cm and `4sqrt3` cm.

Based on the above information, answer the following:

1. Find the length of the longest side of the sandwich.
2. What is the perimeter of the sandwich?
3. If she wants to wrap the sandwich with silver foil, then what area of foil is needed (assuming 10% extra foil needed for folds)?

Answer 1

(i) Length of the longest side:

The longest side of a right-angled triangle is the hypotenuse. Using Pythagoras’ theorem with the given legs a = 4 cm and b = `4sqrt3` cm:

c = `sqrt{4^2 + (4\sqrt{3})^2} = sqrt{16 + 48} = sqrt64` = 8 cm

(ii) Perimeter of the sandwich:

The perimeter is the sum of all three sides of the triangular sandwich:

Perimeter = 4 + `4\sqrt{3} + 8 = (12 + 4\sqrt{3})` cm

(Using `sqrt3` ≈ 1.732, the perimeter is approximately 18.93 cm)

(iii) Area of foil needed:

First, calculate the area of the triangular face of the sandwich:

Area = `1/2` × base × height

= `1/2 \times 4 \times 4\sqrt{3}`

= `8\sqrt{3}\text{ cm}^2`

Adding 10% extra foil for folds:

Total Foil Area =`8\sqrt{3} + 0.10 \times 8\sqrt{3}`

= `1.1 \times 8\sqrt{3}`

= `8.8\sqrt{3}\text{ cm}^2`

(Approximately 15.24 cm²)