Question Video: Applying the Triangle Midsegment Theorem to Solve Problems given the Perimeter Mathematics • First Year of Preparatory School

Video Transcript

The perimeter of square 𝐴𝐵𝐶𝐷 is 352. Find 𝐴𝐹.

All four sides of a square are equal in length. This means that the length of 𝐴𝐵 is equal to 𝐵𝐶, which is equal to 𝐶𝐷, which is equal to 𝐷𝐴. The perimeter of the shape is the distance around the outside. We’re told, in this case, the perimeter of the square is 352. As each of the sides is equal in length, we can divide 352 by four to calculate the length of one side. One way of doing this is using the short division bus stop method. Four does not divide into three, so we carry the three to the tens column.

35 divided by four is equal to eight remainder three. And finally, 32 divided by four is equal to eight. This means that 352 divided by four is equal to 88. The length 𝐴𝐵 on the square is 88 units. The two diagonals 𝐴𝐶 and 𝐵𝐷 meet at the center of the square labeled point 𝑀. As the lines 𝑀𝐹 and 𝐶𝐵 are parallel, point 𝐹 must be halfway between point 𝐴 and point 𝐵. This means that the length 𝐴𝐹 that we’re trying to calculate is a half of 𝐴𝐵. We need to find a half of 88. A half of 80 is 40 and a half of eight is four. Therefore, half of 88 is 44. We can, therefore, conclude that if the perimeter of the square is 352, then the length 𝐴𝐹 is equal to 44.