Paul designed a doghouse to fit against the side of his house. His plan consisted of a right triangle on top of a rectangle. Drag and drop the numbers into the boxes to show the length of each segment.

BD = 37

CE = 36

BE = 42.19

Step-by-step explanation:

AE = BC

    = 22

BC + CD = BD

22 + 15 = 37

BD = 37

The Pythagorean theorem states that in a right-angled triangle

= c² where c is the slant length, a and b are the two dimensions that are perpendicular to each other.

You know the slant length (DE) of a triangle is 39, one of the dimensions (DC) is 15, so you can find the other dimension, CE.

= 39

15² + CE² = 39²

Evaluate.

225 + CE² = 1521

CE² = 1521 - 225

      = 1296

CE =

     = 36

Now that you know the length of CE, you also know the length of AB, since they are equal lengths.

CE = AB

    = 36

We can apply the same formula to find the slant length of the triangle ABE, which is BE.

= BE

= BE

= BE

BE = 42.19 (rounded to 2 d.p.)  

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