Question

To find the length of the diagonal from point A (front/bottom/left) to point G(back/top/right):

You would first use on the bottom of the box rectangle to find the diagonal AC=
Then use CG as of the triangle ACG, with AG being the
AG is approximately =
Word Bank:
square root 73 cm the Pythagorean Theorem the area formula for a rectangle 11 cm the hypotenuse
the perimeter formula for a rectangle 9.4cm a leg 3cm square root 11cm 73 cm 89 cm
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Answer 1

1. the Pythagorean theorem
2. square root 73 cm
3. a leg
4. the hypotenuse
5. 9.4 cm

Explanation:

You want to fill in the blanks regarding the computation of the length of the space diagonal AG.

Pythagorean theorem

The Pythagorean theorem relates the leg lengths to the hypotenuse length of a right triangle. That relation would be used to find AC:

1. You would first use the Pythagorean theorem on the bottom of the box rectangle ...

Using that relation, we find ...

AC² = AB² + BC²

AC² = 8² + 3² = 64 +9 = 73

AC = √73 . . . . cm

2. ... to find the diagonal AC = square root 73 cm.

Again

At this point, we recognize that ∆ACG is a right triangle, and we can use the Pythagorean theorem again.

3. Then use CG as a leg of the triangle ACG, ...

4. ... with AG being the hypotenuse.

Space diagonal

Doing the same sort of computation, we find ...

AG² = AC² +CG²

AG² = (√73)² +4² = 73 +16 = 89

AG = √89 ≈ 9.4

5. AG is approximately = 9.4 cm.

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