Question

using properties of right triangles
exploring the pythagorean theorem
answer these questions about the right triangle
what is the length of the hypotenuse?
what is the area of the hypotenuse square?
what is the area of the square of the leg 8?
what is the area of the square of the leg 6?

Explanation:

Step1: Calculate the area of the square of leg 6

The area of a square is \(side^2\). For side \(6\), the area \(A_1 = 6^2=36\)

Step2: Calculate the area of the square of leg 8

Using the formula \(A = side^2\), for side \(8\), the area \(A_2=8^2 = 64\)

Step3: Calculate the length of the hypotenuse

By the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(a = 6\) and \(b = 8\). So \(c=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}=10\)

Step4: Calculate the area of the hypotenuse square

Using the formula \(A=side^2\), with side \(c = 10\), the area \(A_3=10^{2}=100\)

Answer:

• The area of the square of the leg \(6\): \(36\)
• The area of the square of the leg \(8\): \(64\)
• The length of the hypotenuse: \(10\)
• The area of the hypotenuse square: \(100\)