Question

1) Tanya is buying edging for a triangular flower garden she plans to build in her backyard. If the lengths of the three pieces of edging that she purchases are 13 feet, 10 feet, and 7 feet, will the flower garden be in the shape of a right triangle ?

Answer 1

Converse of the Pythagorean Theorem

The Pythagorean Theorem states that if a triangle is a right triangle, then, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

That is, if a and b are legs and c is the hypotenuse, then

a2 + b2 = c2

The converse of the Pythagorean Theorem states that if a2 + b2 = c2, then the triangle is a right triangle.

Explanation:

Answer 2

The Flower Garden is not in the shape of a right Δ

Explanation:

~ To prove that this garden is in the shape of a right triangle, it can be done so through contradiction ~

Pythagorean Theorem is applied to a right triangle, so we can say that the two legs are 10 and 7 feet, the hypotenuse being 13, knowing it is the longest side;

a^2 + b^2 = c^2,

10^2 + 7^2 = 13^2,

100 + 49 = 169,

149 ≠ 169,

So the Flower Garden will not be in the shape of a right Δ