Question

how do you find the right triangle in the following problem... "Ms. McCoy is planting a garden in the shape of a right triangle. Which of the following sets of Dimensions would make a right triangle?" Answers- A. 10, 8, 7 B. 31, 20, 21 C. 9, 40, 41 D. 11, 13, 5

Answer 1

The correct option is option C

It is the only one that makes a right-angled triangle

Step-by-step explanation:

The dimensions that would make a right angle are the ones with the set of numbers that satisfies the Pythagorean theorem

The Pythagorean theorem state that in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the opposite sides.

Knowing that the hypotenuse is always the longest side

Suppose x is the hypotenuse of a right angled triangle, and y and z are the opposite sides, then

`x^2=y^2+z^2`

Let us check the given options one after the other to see which one is a Pythagorean Triple (satisfies the Pythagorean theorem).

A.

10, 8, 7

`\begin{gathered} 10^2=8^2+7^2 \\ 100=64+49 \\ 100\\e113 \\ \\ \text{Not a Pythagorean triple} \end{gathered}`

B.

31, 20, 21

`\begin{gathered} 31^2=20^2+21^2 \\ 961=400+441 \\ 961\\e841 \\ \\ \text{Not a Pythagorean triple} \end{gathered}`

C.

9, 40, 41

`\begin{gathered} 41^2=40^2+9^2 \\ 1681=1600+81 \\ 1681=1681 \\ \\ \text{ This is a Pythagorean triple} \end{gathered}`

D.

11, 13, 5

`\begin{gathered} 13^2=11^2+5^2 \\ 169=121+25 \\ 169\\e146 \\ \\ \text{Not a Pythagorean triple} \end{gathered}`