Math / Geometry

QuestionFind $W Y$ .
Write your answer in simplified, rationalized form. Do not round.

Studdy Solution

STEP 1

What is this asking? We've got a 45-45-90 triangle, and we know one side.
We need to find the hypotenuse! Watch out! Don't mix up the sides!
Remember the relationships in a 45-45-90 triangle.

STEP 2

1. Set up the ratios
2. Solve for the hypotenuse

STEP 3

In a 45-45-90 triangle, the sides have a special relationship.
If one of the shorter sides is $x$ , then the other shorter side is also $x$ , and the hypotenuse is $x \cdot \sqrt{2}$ !
It's like a magical formula!

STEP 4

We're given that $XY = \sqrt{7}$ .
Since this is one of the shorter sides, we know the other side, $WX$ , is also $\sqrt{7}$ .
We want to find $WY$ , which is the hypotenuse!

STEP 5

We know that the hypotenuse is $x \cdot \sqrt{2}$ , where $x$ is the length of one of the shorter sides.
In our case, $x = \sqrt{7}$ .
So, we just plug it in!

STEP 6

$WY = x \cdot \sqrt{2}$ $WY = \sqrt{7} \cdot \sqrt{2}$ $WY = \sqrt{7 \cdot 2}$ $WY = \sqrt{\textbf{14}}$

STEP 7

The length of $WY$ is $\sqrt{14}$ .
Boom!

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QuestionFind $W Y$ .
Write your answer in simplified, rationalized form. Do not round.

Studdy Solution

STEP 1

What is this asking? We've got a 45-45-90 triangle, and we know one side.
We need to find the hypotenuse! Watch out! Don't mix up the sides!
Remember the relationships in a 45-45-90 triangle.

STEP 2

1. Set up the ratios
2. Solve for the hypotenuse

STEP 3

In a 45-45-90 triangle, the sides have a special relationship.
If one of the shorter sides is $x$ , then the other shorter side is also $x$ , and the hypotenuse is $x \cdot \sqrt{2}$ !
It's like a magical formula!

STEP 4

We're given that $XY = \sqrt{7}$ .
Since this is one of the shorter sides, we know the other side, $WX$ , is also $\sqrt{7}$ .
We want to find $WY$ , which is the hypotenuse!

STEP 5

We know that the hypotenuse is $x \cdot \sqrt{2}$ , where $x$ is the length of one of the shorter sides.
In our case, $x = \sqrt{7}$ .
So, we just plug it in!

STEP 6

$WY = x \cdot \sqrt{2}$ $WY = \sqrt{7} \cdot \sqrt{2}$ $WY = \sqrt{7 \cdot 2}$ $WY = \sqrt{\textbf{14}}$

STEP 7

The length of $WY$ is $\sqrt{14}$ .
Boom!

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QuestionFind WYW YWY.Write your answer in simplified, rationalized form. Do not round.

Studdy Solution

STEP 1

What is this asking? We've got a 45-45-90 triangle, and we know one side.We need to find the hypotenuse! Watch out! Don't mix up the sides!Remember the relationships in a 45-45-90 triangle.

STEP 2

1. Set up the ratios2. Solve for the hypotenuse

STEP 3

In a 45-45-90 triangle, the sides have a special relationship.If one of the shorter sides is xxx, then the other shorter side is also xxx, and the hypotenuse is x⋅2x \cdot \sqrt{2}x⋅2​!It's like a magical formula!

STEP 4

We're given that XY=7XY = \sqrt{7}XY=7​.Since this is one of the shorter sides, we know the other side, WXWXWX, is *also* 7\sqrt{7}7​.We want to find WYWYWY, which is the **hypotenuse**!

STEP 5

We know that the hypotenuse is x⋅2x \cdot \sqrt{2}x⋅2​, where xxx is the length of one of the shorter sides.In our case, x=7x = \sqrt{7}x=7​.So, we just plug it in!

STEP 6

WY=x⋅2WY = x \cdot \sqrt{2}WY=x⋅2​ WY=7⋅2WY = \sqrt{7} \cdot \sqrt{2}WY=7​⋅2​ WY=7⋅2WY = \sqrt{7 \cdot 2}WY=7⋅2​WY=14WY = \sqrt{\textbf{14}}WY=14​

STEP 7

The length of WYWYWY is 14\sqrt{14}14​.Boom!

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Start learning now

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

QuestionFind $W Y$ .
Write your answer in simplified, rationalized form. Do not round.

What is this asking? We've got a 45-45-90 triangle, and we know one side.
We need to find the hypotenuse! Watch out! Don't mix up the sides!
Remember the relationships in a 45-45-90 triangle.

1. Set up the ratios
2. Solve for the hypotenuse

In a 45-45-90 triangle, the sides have a special relationship.
If one of the shorter sides is $x$ , then the other shorter side is also $x$ , and the hypotenuse is $x \cdot \sqrt{2}$ !
It's like a magical formula!

We're given that $XY = \sqrt{7}$ .
Since this is one of the shorter sides, we know the other side, $WX$ , is also $\sqrt{7}$ .
We want to find $WY$ , which is the hypotenuse!

We know that the hypotenuse is $x \cdot \sqrt{2}$ , where $x$ is the length of one of the shorter sides.
In our case, $x = \sqrt{7}$ .
So, we just plug it in!

$WY = x \cdot \sqrt{2}$ $WY = \sqrt{7} \cdot \sqrt{2}$ $WY = \sqrt{7 \cdot 2}$ $WY = \sqrt{\textbf{14}}$

The length of $WY$ is $\sqrt{14}$ .
Boom!