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Pythagorean theorem word problem: carpet

CCSS.Math:

Video transcript

a carpet measures seven feet long and has a diagonal measurement of square root of 74 feet find the width of the carpet so let's draw ourselves a carpet here so let's draw a carpet it has a length of 7 feet so let's say that that is 7 feet right there and it's going to be a rectangle of some kind so let's say that this is we're looking down on the carpet like that that's our carpet and then it has a diagonal measurement of square root of 74 feet a diagonal measurement so that means that this distance right here draw a little bit neater than that this distance right here the diagonal of the carpet is the square root of 74 feet and what they want to know is the width of the carpet find the width of the carpet so let's say that this is the width of the carpet carpet that is W right there now you might already realize that what I've drawn here is a right triangle let me make sure yeah you realize it this is a 90 degree angle here and since that is a triangle that has a 90 degree angle it's a right triangle the side opposite the right angle or the 90 degrees is the hypotenuse or the longest side it is the square root of 74 and the shorter sides are W and 7 and the Pythagorean theorem tells us that the sum of the squares of the shorter side will be equal to the square of the hypotenuse or the square of the longest side so we get W squared this side squared plus 7 squared plus 7 squared this other side squared is going to be equal to the hypotenuse squared square root of 74 squared and then we get W squared plus 49 is equal to the square root of 74 squared well that's just going to be 74 is equal to 74 we can subtract 49 from both sides of this equation so we have just a W squared on the left hand side subtract 49 from both sides the left side these guys are going to cancel out we're just going to be left with w squared is equal to what's 74 - 49 74 - 49 well we could do a little bit of regrouping or borrowing here if we don't want to do it in our head you can make this a 14 this becomes a 6 14 minus 9 is 5 6 minus 4 is 2 and we have W squared is equal to 25 so W is going to be equal to the square root of 25 the positive square root so let's take the square root of both sides the positive square root and we will get W is equal to 5 because we want obviously we don't want it to be negative 5 that wouldn't be a realistic distance so the width of the carpet is 5 and we're done