Question

from a square piece of cartolina with a side of 60cm liza cut the biggest cross what is the area of the cross?

Answer 1

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Answer 2

Given :- from a square piece of cartolina with a side of 60cm liza cut the biggest cross what is the area of the cross ?

Solution :-

Let us assume that, width of the biggest cross is x cm .

since a cross is formed when we make 9 quadrilateral inside and remove 4 corners quadrilateral . so, rest 5 quadrilateral will form a biggest cross .

now,

→ Area of middle quadrilateral = x * x = x²

and,

→ Area of 4 quadrilateral formed at middle = 4[x * (60 - x)] = (240x - 4x²)

so,

→ Total area of cross = A = x² + 240x - 4x² = (240x - 3x²)

now, differentiate with respect to x,

→ A' = 240 - 6x

putting A' = 0, we get,

→ 240 - 6x = 0

→ 6x = 240

→ x = 40

therefore,

→ Area of cross = (240x - 3x²)

→ A = 240 * 40 - 3 * (40)²

→ A = 9600 - 4800

→ A = 4800 cm² (Ans.)

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