the video and then solve the problem given below. here to watch the video. econd side of a triangular deck is 3 feet longer than the shortest side. The third side of the deck is 3 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 76 feet, what shortest side of the deck is plify your answer.)

To solve for the shortest side of the deck, let’s denote it as \( x \). According to the problem, the second side is \( x + 3 \) feet, and the third side is \( 2x - 3 \) feet. The perimeter of the triangle is the sum of all its sides: \[ x + (x + 3) + (2x - 3) = 76 \] Now, simplify: \[ x + x + 3 + 2x - 3 = 76 \] \[ 4x = 76 \] Divide both sides by 4: \[ x = 19 \] So, the shortest side of the deck is 19 feet! The second side measures \( 19 + 3 = 22 \) feet, and the third side measures \( 2(19) - 3 = 35 \) feet. Adding those gives: \[ 19 + 22 + 35 = 76 \] Perfect! Everything checks out. --- In ancient times, triangles were not just shapes; they were vital in architecture and civil engineering! The Pythagorean theorem, discovered by the Greeks, was originally used to help build the sturdy foundations of temples and homes. This relationship between the sides of right triangles made it possible to create beautiful and enduring structures. Geometry principles like those involved in calculating the sides of triangles are incredibly useful in real-world applications! Architects and engineers use these concepts daily, whether they're designing a stunning triangular roof, crafting stable bridges, or calculating land plots. Knowing the lengths of sides helps ensure stability and aesthetic appeal in structures we see around us every day!