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Answer attached question, show full working and explain what you are doing in each step

Answer attached question, show full working and explain what you are doing in each-example-1

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Answer:

the required equation is x² -10x +18 = 0

Explanation:

Given side x and diagonal 8 cm of a rectangle with perimeter 20 cm, you want to show that the value of x satisfies an equation of the form ...

x² +ax +b = 0 . . . . . where a and b are integers.

Perimeter

The perimeter is the sum of the side lengths. It can be expressed by the formula ...

P = 2(L +W)

Solving for W gives ...

W = P/2 -L

For the given rectangle, the width is ...

W = 20/2 -x = 10 -x

Diagonal

The length of the diagonal is related to the length and width of the rectangle by the Pythagorean theorem.

c² = a² +b²

8² = x² +(10 -x)² = 2x² -20x +100

32 = x² -10x +50 . . . . . . . . divide by 2

x² -10x +18 = 0 . . . . . . . . . . subtract 32

This shows that x must satisfy a quadratic of the form x² +ax +b = 0, where a=-10, and b=18, both integers.

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Additional comment

The vertex form of the equation is ...

(x -5)² -7 = 0

This has solutions ...

x = 5 ±√7 ≈ {2.354, 7.646} . . . . centimeters

User Jagdeesh Kumar
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