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 $4\sqrt{3}$ cm.

Based on the above information, answer the following:

(i) Find the length of the longest side of the sandwich.

(ii) What is the perimeter of the sandwich ?

(iii) If she wants to wrap the sandwich with silver foil, then what area of foil is needed (assuming 10% extra foil needed for folds) ?

Given,

Right-angled triangle :

One side = 4 cm

Other side = $4\sqrt{3}$ cm

(i) Length of the longest side = Hypotenuse of the triangle

Using Pythagoras theorem,

Hypotenuse² = (4)² + ($4\sqrt{3}$)²

Hypotenuse² = 16 + 16 × 3

Hypotenuse² = 16 + 48

Hypotenuse² = 64

Hypotenuse = $\sqrt{64}$

Hypotenuse = 8 cm.

Hence, length of the longest side = 8 cm.

(ii) Perimeter of the sandwich = sum of all sides

= 4 + $4\sqrt{3}$ + 8

= 12 + 6.928

= 18.928 ≈ 18.93 cm.

Hence, perimeter = 18.93 cm.

(iii) By formula,

Area of traingle = $\dfrac{1}{2}$ × Base × Height

= $\dfrac{1}{2} × 4 × 4\sqrt{3}$

= $8\sqrt{3}$

= 13.86 cm².

Area of foil needed = 13.86 + 10% of 13.86

= 13.86 + 1.386

= 15.246

= 15.25 cm².

Hence, area of foil needed = 15.25 cm².