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Answer :
The height of the rectangle is approximately 14.0 inches when rounded to 1 decimal place. This is determined using the Pythagorean theorem and solving the resulting quadratic equation. The width is 5 inches longer than the height, and the diagonal measurement is 59 inches.
Let's denote the height of the rectangle as (h) inches. According to the given information, the width is 5 inches longer than the height, so the width can be represented as (w = h + 5) inches.
The diagonal of the rectangle forms a right triangle with the height and width. Using the Pythagorean theorem: [tex]\(h^2 + (h + 5)^2 = 59^2\).[/tex]
Solving this equation:
[tex]\(h^2 + h^2 + 10h + 25 = 3481\),[/tex]
[tex]\(2h^2 + 10h - 3456 = 0\).[/tex]
Dividing by 2:
[tex]\(h^2 + 5h - 1728 = 0\).[/tex]
Solving this quadratic equation, we find (h approx 13.959), rounded to 1 decimal place.
The height of the rectangle is approximately 14.0 inches, rounded to 1 decimal place. This height, along with the given width relationship and diagonal measurement, satisfies the conditions of the problem.
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