Using the Pythagorean Theorem, it is found that:
a) The hypotenuse is of 9.49 cm.
b) The new area of the triangle is of 30 cm².
What is the Pythagorean Theorem?
The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
For this problem, the sides are given as follows:
3 cm and 9 cm.
Hence the hypotenuse is given by:
h² = 3² + 9²
h = sqrt(3² + 9²)
h = 9.49 cm.
The hypotenuse is of 9.49 cm.
What is the area of a right triangle?
The area of a right triangle of sides a and b is given by half the multiplication of the sides, as follows:
A = 0.5ab.
For this problem, we have that:
- The side of 3 cm is increased by 2 cm, hence a = 5 cm.
- The side of 9 cm is increased by 3 cm, hence b = 12 cm.
Then:
A = 0.5 x 5 x 12 = 30 cm².
The new area of the triangle is of 30 cm².
More can be learned about the Pythagorean Theorem at https://brainly.com/question/343682
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