Question

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.

Answer 1

BD = 37

CE = 36

BE = 42.19

Explanation:

AE = BC

= 22

BC + CD = BD

22 + 15 = 37

BD = 37

The Pythagorean theorem states that in a right-angled triangle

`\sqrt{a^(2)+b^(2) }` = 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.

`\sqrt{15^(2)+CE^(2)}` = 39

15² + CE² = 39²

Evaluate.

225 + CE² = 1521

CE² = 1521 - 225

= 1296

CE =
`√(1296)`

= 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.

`\sqrt{22^(2)+36^(2) }` = BE

`√(484+1296)` = BE

`√(1780)` = BE

BE = 42.19 (rounded to 2 d.p.)