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Triangle A and Triangle B are right triangles.
Triangle A has a height of 8 meters and a base of 6 meters.
Triangle B has a height that is one unit greater than triangle A and a base that is one unit less.
What is the measure of the hypotenuse of triangle A? Show your work.
Determine if the hypotenuse of triangle B has the same hypotenuse as triangle A. Justify your solution.

Answer :

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I. The measure of the hypotenuse of triangle A is equal to 10 meters.

II. The measure of the hypotenuse of triangle B is equal to 10.30 meters.

Given the following data:

  • Height A = 8 meters
  • Base A = 6 meters

To determine the measure of the hypotenuse of triangle A, we would apply Pythagorean's theorem since the is a right triangle:

Mathematically, Pythagorean's theorem is given by the formula:

[tex]C^2 = A^2 + B^2\\\\C^2 = 6^2 + 8^2\\\\C^2=36+64\\\\C^2 = 64+36\\\\C^2=100\\\\C=\sqrt{100}[/tex]

Hypotenuse, C = 10 meters.

For Triangle B:

Triangle B has a height that is one (1) unit greater than triangle A:

Height B = 8 + 1 = 9 meters

Triangle B has a base that is one (1) unit less than triangle A:

Base B = 6 - 1 = 5 meters

To find the hypotenuse B:

[tex]C^2 = A^2 + B^2\\\\C^2 = 5^2 + 9^2\\\\C^2=25+81\\\\C^2=106\\\\C=\sqrt{106}[/tex]

Hypotenuse, C = 10.30 meters

From the above calculations , we can deduce that the measure of the hypotenuse of both Triangle A and Triangle B are different.

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