A triangle has sides with lengths of 8 feet, 15 feet, and 17 feet. Is it a right triangle? Choices: (A)yes (B)no

Identify sides and longest side: Step 1: Identify the sides of the triangle and the longest side which could be the hypotenuse. Given sides are 8 ft, 15 ft, and 17 ft. The longest side is 17 ft, which could be the hypotenuse if it's a right triangle. Apply Pythagorean Theorem: Step 2: Apply the Pythagorean Theorem to check if it's a right triangle. According to the Pythagorean Theorem, for a right triangle with legs a and b, and hypotenuse c, the equation is a^2 + b^2 = c^2. Here, let's check if 8^2 + 15^2 = 17^2. Calculate squares of sides: Step 3: Calculate the squares of the sides. 8^2 = 64, 15^2 = 225, and 17^2 = 289. Add squares and compare: Step 4: Add the squares of the shorter sides and compare with the square of the longest side. 64 + 225 = 289. Now, compare this with 17^2. 289 = 289. Conclude right triangle: Step 5: Conclude if the triangle is a right triangle based on the calculations. Since the sum of the squares of the two shorter sides equals the square of the longest side, the triangle is a right triangle.

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A triangle has sides with lengths of $8\,\text{feet}$ , $15\,\text{feet}$ , and $17\,\text{feet}$ . Is it a right triangle? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Math Problems

Grade 8

Converse of the Pythagorean theorem: is it a right triangle?

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Q. A triangle has sides with lengths of

8\,\text{feet}

15\,\text{feet}

, and

17\,\text{feet}

. Is it a right triangle?

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Identify sides and longest side: Step $1$ : Identify the sides of the triangle and the longest side which could be the hypotenuse. Given sides are $8\,\text{ft}$ , $15\,\text{ft}$ , and $17\,\text{ft}$ . The longest side is $17\,\text{ft}$ , which could be the hypotenuse if it's a right triangle.
Apply Pythagorean Theorem: Step $2$ : Apply the Pythagorean Theorem to check if it's a right triangle. $\newline$ According to the Pythagorean Theorem, for a right triangle with legs $a$ and $b$ , and hypotenuse $c$ , the equation is $a^2 + b^2 = c^2$ . Here, let's check if $8^2 + 15^2 = 17^2$ .
Calculate squares of sides: Step $3$ : Calculate the squares of the sides. $\newline$ $8^2 = 64$ , $15^2 = 225$ , and $17^2 = 289$ .
Add squares and compare: Step $4$ : Add the squares of the shorter sides and compare with the square of the longest side. $\newline$ $64 + 225 = 289$ . Now, compare this with $17^2$ . $\newline$ $289 = 289$ .
Conclude right triangle: Step extbf{ $5$ }: Conclude if the triangle is a right triangle based on the calculations. $\newline$ Since the sum of the squares of the two shorter sides equals the square of the longest side, the triangle is a right triangle.