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QuestionTrova il lato di un quadrato isoperimetrico a un rettangolo di base 15 cm15 \mathrm{~cm} e altezza 24 cm24 \mathrm{~cm}. R: 19,5 cm19,5 \mathrm{~cm}. Inoltre, la somma e la differenza di due lati consecutivi di un rettangolo sono 75 cm75 \mathrm{~cm} e 17 cm17 \mathrm{~cm}.

Studdy Solution

STEP 1

Assumptions1. The rectangle has a base of15 cm and a height of24 cm. . The square is isoperimetric to the rectangle, meaning they have the same perimeter.
3. The sum of two consecutive sides of a rectangle is75 cm and the difference is17 cm.

STEP 2

First, we need to find the perimeter of the rectangle. The perimeter of a rectangle is given by the formulaPerimeter=2×(base+height)Perimeter =2 \times (base + height)

STEP 3

Now, plug in the given values for the base and height to calculate the perimeter of the rectangle.
Perimeter=2×(15 cm+24 cm)Perimeter =2 \times (15\,cm +24\,cm)

STEP 4

Calculate the perimeter of the rectangle.
Perimeter=2×(15 cm+24 cm)=78 cmPerimeter =2 \times (15\,cm +24\,cm) =78\,cm

STEP 5

Now that we have the perimeter of the rectangle, we know that the perimeter of the square is the same, since they are isoperimetric. The perimeter of a square is given by the formulaPerimeter=4×sidePerimeter =4 \times side

STEP 6

We can rearrange this formula to find the length of the side of the squareside=Perimeter/4side = Perimeter /4

STEP 7

Plug in the value for the perimeter to calculate the side length of the square.
side=78 cm/4side =78\,cm /4

STEP 8

Calculate the side length of the square.
side=78 cm/4=19.5 cmside =78\,cm /4 =19.5\,cmThe side of the square is19.5 cm.

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