Math / Geometry

QuestionSolve for the legs of the 45-45-90 triangle. a. $x=5$ and $y=5$ b. $x=5$ and $y=5 \sqrt{2}$ c. $x=5 \sqrt{2}$ and $y=5$ d. $x=5 \sqrt{2}$ and $y=5 \sqrt{2}$

Studdy Solution

STEP 1

1. We are dealing with a 45-45-90 triangle, which is a special type of isosceles right triangle.
2. In a 45-45-90 triangle, the legs are equal, and the hypotenuse is $\text{leg} \times \sqrt{2}$ .

STEP 2

1. Identify the correct relationship between the legs and the hypotenuse for a 45-45-90 triangle.
2. Evaluate each option to determine which one satisfies the properties of a 45-45-90 triangle.

STEP 3

In a 45-45-90 triangle, the legs are equal, and the hypotenuse is $\text{leg} \times \sqrt{2}$ .

STEP 4

Evaluate option a: $x = 5$ and $y = 5$ .
- Both legs are equal, which satisfies the condition for a 45-45-90 triangle. - However, the hypotenuse should be $5\sqrt{2}$ , not $5$ .
This option does not satisfy the properties of a 45-45-90 triangle.

STEP 5

Evaluate option b: $x = 5$ and $y = 5\sqrt{2}$ .
- One leg is $5$ , and the other is $5\sqrt{2}$ . - The hypotenuse should be $5\sqrt{2}$ , but both legs should be equal.
This option does not satisfy the properties of a 45-45-90 triangle.

STEP 6

Evaluate option c: $x = 5\sqrt{2}$ and $y = 5$ .
- One leg is $5\sqrt{2}$ , and the other is $5$ . - The hypotenuse should be $5\sqrt{2}$ , but both legs should be equal.
This option does not satisfy the properties of a 45-45-90 triangle.

STEP 7

Evaluate option d: $x = 5\sqrt{2}$ and $y = 5\sqrt{2}$ .
- Both legs are equal, which satisfies the condition for a 45-45-90 triangle. - The hypotenuse should be $5\sqrt{2} \times \sqrt{2} = 10$ .
This option satisfies the properties of a 45-45-90 triangle.
The correct option that satisfies the properties of a 45-45-90 triangle is:
$\boxed{d}$

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QuestionSolve for the legs of the 45-45-90 triangle. a. $x=5$ and $y=5$ b. $x=5$ and $y=5 \sqrt{2}$ c. $x=5 \sqrt{2}$ and $y=5$ d. $x=5 \sqrt{2}$ and $y=5 \sqrt{2}$

Studdy Solution

STEP 1

1. We are dealing with a 45-45-90 triangle, which is a special type of isosceles right triangle.
2. In a 45-45-90 triangle, the legs are equal, and the hypotenuse is $\text{leg} \times \sqrt{2}$ .

STEP 2

1. Identify the correct relationship between the legs and the hypotenuse for a 45-45-90 triangle.
2. Evaluate each option to determine which one satisfies the properties of a 45-45-90 triangle.

STEP 3

In a 45-45-90 triangle, the legs are equal, and the hypotenuse is $\text{leg} \times \sqrt{2}$ .

STEP 4

Evaluate option a: $x = 5$ and $y = 5$ .
- Both legs are equal, which satisfies the condition for a 45-45-90 triangle. - However, the hypotenuse should be $5\sqrt{2}$ , not $5$ .
This option does not satisfy the properties of a 45-45-90 triangle.

STEP 5

Evaluate option b: $x = 5$ and $y = 5\sqrt{2}$ .
- One leg is $5$ , and the other is $5\sqrt{2}$ . - The hypotenuse should be $5\sqrt{2}$ , but both legs should be equal.
This option does not satisfy the properties of a 45-45-90 triangle.

STEP 6

Evaluate option c: $x = 5\sqrt{2}$ and $y = 5$ .
- One leg is $5\sqrt{2}$ , and the other is $5$ . - The hypotenuse should be $5\sqrt{2}$ , but both legs should be equal.
This option does not satisfy the properties of a 45-45-90 triangle.

STEP 7

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QuestionSolve for the legs of the 45-45-90 triangle. a. x=5x=5x=5 and y=5y=5y=5 b. x=5x=5x=5 and y=52y=5 \sqrt{2}y=52​ c. x=52x=5 \sqrt{2}x=52​ and y=5y=5y=5 d. x=52x=5 \sqrt{2}x=52​ and y=52y=5 \sqrt{2}y=52​

Studdy Solution

STEP 1

1. We are dealing with a 45-45-90 triangle, which is a special type of isosceles right triangle.2. In a 45-45-90 triangle, the legs are equal, and the hypotenuse is leg×2 \text{leg} \times \sqrt{2} leg×2​.

STEP 2

1. Identify the correct relationship between the legs and the hypotenuse for a 45-45-90 triangle.2. Evaluate each option to determine which one satisfies the properties of a 45-45-90 triangle.

STEP 3

In a 45-45-90 triangle, the legs are equal, and the hypotenuse is leg×2 \text{leg} \times \sqrt{2} leg×2​.

STEP 4

Evaluate option a: x=5 x = 5 x=5 and y=5 y = 5 y=5.- Both legs are equal, which satisfies the condition for a 45-45-90 triangle. - However, the hypotenuse should be 52 5\sqrt{2} 52​, not 5 5 5.This option does not satisfy the properties of a 45-45-90 triangle.

STEP 5

Evaluate option b: x=5 x = 5 x=5 and y=52 y = 5\sqrt{2} y=52​.- One leg is 5 5 5, and the other is 52 5\sqrt{2} 52​. - The hypotenuse should be 52 5\sqrt{2} 52​, but both legs should be equal.This option does not satisfy the properties of a 45-45-90 triangle.

STEP 6

Evaluate option c: x=52 x = 5\sqrt{2} x=52​ and y=5 y = 5 y=5.- One leg is 52 5\sqrt{2} 52​, and the other is 5 5 5. - The hypotenuse should be 52 5\sqrt{2} 52​, but both legs should be equal.This option does not satisfy the properties of a 45-45-90 triangle.

STEP 7

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve for the legs of the 45-45-90 triangle. a. $x=5$ and $y=5$ b. $x=5$ and $y=5 \sqrt{2}$ c. $x=5 \sqrt{2}$ and $y=5$ d. $x=5 \sqrt{2}$ and $y=5 \sqrt{2}$

1. We are dealing with a 45-45-90 triangle, which is a special type of isosceles right triangle.
2. In a 45-45-90 triangle, the legs are equal, and the hypotenuse is $\text{leg} \times \sqrt{2}$ .

1. Identify the correct relationship between the legs and the hypotenuse for a 45-45-90 triangle.
2. Evaluate each option to determine which one satisfies the properties of a 45-45-90 triangle.

In a 45-45-90 triangle, the legs are equal, and the hypotenuse is $\text{leg} \times \sqrt{2}$ .

Evaluate option a: $x = 5$ and $y = 5$ .
- Both legs are equal, which satisfies the condition for a 45-45-90 triangle. - However, the hypotenuse should be $5\sqrt{2}$ , not $5$ .
This option does not satisfy the properties of a 45-45-90 triangle.

Evaluate option b: $x = 5$ and $y = 5\sqrt{2}$ .
- One leg is $5$ , and the other is $5\sqrt{2}$ . - The hypotenuse should be $5\sqrt{2}$ , but both legs should be equal.
This option does not satisfy the properties of a 45-45-90 triangle.

Evaluate option c: $x = 5\sqrt{2}$ and $y = 5$ .
- One leg is $5\sqrt{2}$ , and the other is $5$ . - The hypotenuse should be $5\sqrt{2}$ , but both legs should be equal.
This option does not satisfy the properties of a 45-45-90 triangle.