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Answer :
Final answer:
To find the dimensions of the rectangle, we define the width as w, leading to expressions for the length and diagonal in terms of w. We then apply the Pythagorean theorem to these expressions and solve for w to determine the rectangle's dimensions.
Explanation:
To solve for the dimensions of the rectangle, we are given that the length of a rectangle is 59 inches greater than twice the width, and the diagonal is 2 inches more than the length. Let's denote the width of the rectangle as w inches. Consequently, the length, l, would be l = 2w + 59 inches. The diagonal, denoted by d, would then be d = l + 2 = 2w + 59 + 2 = 2w + 61 inches.
Since we are working with a rectangle, we can apply the Pythagorean theorem which states that a² + b² = c², where a and b are the lengths of the shorter sides and c is the length of the diagonal. Using this theorem, we set up an equation:w² + l² = d² , substituting the expressions we have for l and d.
w² + (2w + 59)² = (2w + 61)². Expanding this equation and simplifying will allow us to solve for w, the width of the rectangle. Once we find w, we can calculate l and d using the above relationships.
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Final answer:
The dimensions of the rectangle are 2 inches by 63 inches.
Explanation:
To find the dimensions of the rectangle, we can use the given information:
- The length is 59 inches greater than twice the width.
- The diagonal is 2 inches more than the length.
Let's assume the width of the rectangle is 'w'.
Then, the length of the rectangle is 2w + 59 inches.
Using the Pythagorean theorem, we can set up the following equation for the diagonal:
w^2 + (2w + 59)^2 = (2w + 59)^2 + 2^2
Simplifying the equation, we get:
w^2 = 4
Therefore, the width of the rectangle is 2 inches.
Substituting this value into the equation for the length, we get:
Length = 2(2) + 59 = 4 + 59 = 63 inches
So, the dimensions of the rectangle are 2 inches by 63 inches.
