You have hired a contractor to build a house. The rectangular foundation (the concrete slab that the house is built on) has just been finished. You want to make sure that the construction is done well and the foundation is square, so you decide to see if the corners are right angles. You measure the width of the foundation to be 30 feet, the length to be 72 feet and the diagonal to be 78 feet. Did the company build the foundation with right angles? Prove your answer (show your work)

Question

Aurora

Mathematics

4 November, 04:33

You have hired a contractor to build a house. The rectangular foundation (the concrete slab that the house is built on) has just been finished. You want to make sure that the construction is done well and the foundation is square, so you decide to see if the corners are right angles. You measure the width of the foundation to be 30 feet, the length to be 72 feet and the diagonal to be 78 feet. Did the company build the foundation with right angles? Prove your answer (show your work)

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Answers (1)

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Tobias Burton · Answer 1

Step-by-step explanation:

A right angle triangle would be formed with the width of the foundation being the opposite side, length being the adjacent side and diagonal being the hypotenuse. To determine if the company built the foundation with right angles, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore,

78² = 30² + 72²

6084 = 900 + 5184

6084 = 6084

Therefore, the company built the foundation with right angles