Question Video: Applying Pythagoras’s Theorem to Solve Complex Problems in Real-Life Contexts Mathematics • 8th Grade

The figure shows a 129 m long bridge on supports 𝑀𝐢, 𝑀𝐷 attached at the midpoint 𝑀. If 𝐴𝐢 = 51.6 m, find the length of 𝑀𝐢 to the nearest hundredth.


Video Transcript

The figure shows a 129-meter long bridge on supports 𝑀𝐢 and 𝑀𝐷 attached at the midpoint 𝑀. If 𝐴𝐢 is equal to 51.6 meters, find the length of 𝑀𝐢 to the nearest hundredth.

We are told in the question that the length of the bridge 𝐴𝐡 is 129 meters. As 𝑀 is the midpoint of 𝐴𝐡, we can calculate the distance 𝐴𝑀 by dividing 129 by two. This is equal to 64.5 meters. We are also told that the length 𝐴𝐢 is 51.6 meters. 𝐴𝑀𝐢 is a right triangle where we know two lengths and need to calculate the length 𝑀𝐢.

We can do this using the Pythagorean theorem. This states that π‘Ž squared plus 𝑏 squared is equal to 𝑐 squared. 𝑐 is the longest side of the right triangle, known as the hypotenuse. In this case, this is the length 𝑀𝐢. Substituting in our values gives us 64.5 squared plus 51.6 squared is equal to π‘₯ squared. Typing the left-hand side into our calculator gives us 6822.81. We can then square root both sides of this equation to calculate the value of π‘₯. π‘₯ is equal to 62.600302 [82.600302] and on so.

We are asked to round to the nearest hundredth, which is the same as rounding to two decimal places. As this rounds down, the length of 𝑀𝐢, to the nearest hundredth, is 82.60 meters.

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