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a builder needs to add cross braces to a 3.5 metre by 5 meter opening between supports in a building as shown in the figure above okay so this is 3.5 meters high 5 metres wide and then this right over here is a cross brace so that right over there's a cross brace there's another one that goes that way so which of the following is closest to the length of one of the Cross braces and they give us four options here and so let's look at this so closest to the length of one of the Cross braces so if you look at the cross brace that I have started to shade in here in this navy blue you see if you look at that and then if you look at this 5 meter side so let me do this in a brighter color if you look at this and then you look at this 5 meter side and then you look at this 3.5 meter side you see that they form a right triangle and so if we wanted to solve for the length of the cross brace that cross brace is a hypotenuse of the right triangle it's the longest side of that right triangle and so we know that we cannot put we can apply the Pythagorean theorem here we know the Pathet where the Pythagorean theorem tells us that the length of the sum of the two shorter side squared so five squared plus three point five squared is going to be length is going to be equal to the length of the hypotenuse squared so let's just call this length H is going to or actually we could call it C for used to using the Pythagorean theorem calling this ABC and say a squared plus B squared is equal to let's call that C C for cross braces is equal to C squared now v squared is pretty straight it's pretty straight forward that's going to be 25 now 3.5 squared let's see 3.5 times 3.5 5 times 5 is 25 3 times 5 is 15 plus 2 is 17 now I'm gonna multis the 3 3 times 5 is 15 deep 3 times 3 is 9 plus 1 is 10 5 plus 0 is 5 7 plus 5 is 12 1 plus 1 is 2 and then you have one right over here and you have two digits to the right of the decimal points you're gonna have two digits to the right of the decimal point right over here so this is going to be plus twelve plus 12.25 is equal to C squared now 25 plus 12.25 that's going to be thirty seven point two five is equal to C squared or we could say that C is equal to the square root of thirty-seven point two five now let's think about what this is we know that six squared is equal to 36 and we know that seven squared is equal to 49 so C is going to be between we know that C two actually let me write this down so let's see we know that let me give us give ourselves some more space six squared is equal to 36 and seven squared is equal to 49 and we know that C squared is equal to 37 0.25 which is closer to 36 it's larger than 36 but it's closer to 36 and it is 249 so I'd approximate C would be between 6 & 7 and it's gonna be closer to 6 and so let's see out of our options right over here 6.1 looking pretty good it's definitely not gonna be eight point five eight point five squared is going to be greater than 64 so it's not gonna be that three point six meters squared well that's going to be less than 16 so six point one's looking good this is gonna be a little bit more than 36 which 37 point two five is a little bit more than 36