Final answer:
To find the values of x for which the length of the diagonal of the new rectangle is greater than 13 cm, use the Pythagorean theorem and solve a quadratic inequality.
Step-by-step explanation:
To find the values of x for which the length of the diagonal of the new rectangle is greater than 13 cm, we need to use the Pythagorean theorem. The diagonal forms the hypotenuse of a right triangle with the sides of the rectangle as the other two sides. Let's denote the increase in dimensions as x. So, the length and width of the new rectangle are 3 cm + x and 10 cm + x respectively.
By applying the Pythagorean theorem, we get:
(3 cm + x)2 + (10 cm + x)2 > 132
Expanding and simplifying this equation will give us a quadratic inequality that we can solve to find the valid range of x values.
After solving the quadratic inequality, we find that the value range for x is (-∞, 2]. Therefore, for any values of x, less than or equal to 2, the length of the diagonal of the new rectangle will be greater than 13 cm.
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