Respuesta :
Using area of a rectangle, it is found that the area of the iPad's screen is of 45.2 square inches.
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The area of a rectangle of length l and width w is given by:
[tex]A = lw[/tex]
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The diagonal of a rectangle is the hypotenuse of a right triangle, in which the sides are the length and the width.
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- The first step before finding the area is finding the length and the width.
- The ratio of length to width is 4:3, thus, [tex]w = x, l = \frac{4x}{3}[/tex]
- The diagonal, which is the hypotenuse of a right triangle in which w and l are the sides, is 9.7, and thus, applying the Pythagorean Theorem:
[tex]x^2 + (\frac{4x}{3})^2 = (9.7)^2[/tex]
[tex]x^2 + \frac{16x^2}{9} = 94.09[/tex]
Multiplying everything by 9:
[tex]9x^2 + 16x^2 = 846.81[/tex]
[tex]25x^2 = 846.81[/tex]
[tex]x^2 = \frac{846.81}{25}[/tex]
[tex]x = \sqrt{\frac{846.81}{25}}[/tex]
[tex]x = 5.82[/tex]
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- The width is of [tex]w = 5.82[/tex]
- The length is of [tex]l = \frac{4}{3}(5.82) = 7.76[/tex]
- Thus, the area is:
[tex]A = lw = 7.76(5.82) = 45.2[/tex]
The area of the iPad's screen is of 45.2 square inches.
A similar problem is given at https://brainly.com/question/10489198
