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Suppose you want to draw a rectangle where the width is 1 centimeter more than the length, and the diagonal is 2 centimeters longer than the length. What are the dimensions of the rectangle?

A) Length = 3 cm, Width = 4 cm
B) Length = 4 cm, Width = 5 cm
C) Length = 5 cm, Width = 6 cm
D) Length = 6 cm, Width = 7 cm

User Vishal G
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1 Answer

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Final answer:

The dimensions of the rectangle are Length = 3 cm and Width = 4 cm.

Step-by-step explanation:

To solve this problem, let's assume the length of the rectangle is 'x' centimeters.

According to the given information, the width is 1 centimeter more than the length, so the width is 'x + 1' centimeters.

The diagonal is 2 centimeters longer than the length, so the diagonal is 'x + 2' centimeters.

Using the Pythagorean theorem for a right triangle (where the length, width, and diagonal form the sides of the triangle), we have:

x2 + (x + 1)2 = (x + 2)2

Simplifying this equation, we get:

x2 + x2 + 2x + 1 = x2 + 4x + 4

Combining like terms, we have:

2x2 + 2x + 1 = x2 + 4x + 4

x2 - 2x - 3 = 0

Factoring or using the quadratic formula, we find that x = 3 or x = -1.5. Since the length cannot be negative, we take x = 3. Therefore, the length of the rectangle is 3 centimeters and the width is 3 + 1 = 4 centimeters.

User WebBrother
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