Math / Algebra

Question\begin{align} 2y + 2 &= 5 \\ \end{align}

Studdy Solution

STEP 1

1. We assume that the larger triangle and the smaller triangle are similar, given that they share a right angle and have proportional sides.
2. We assume that the lengths given in the problem are accurate and can be used to set up a proportion.
3. The goal is to find the length of the base of the larger triangle, which is labeled as $y$ .

STEP 2

1. Set up a proportion based on the similarity of the triangles.
2. Solve the proportion to find the value of $y$ .
3. Verify the solution by checking if it satisfies the given conditions.

STEP 3

Since the triangles are similar, the ratio of corresponding sides must be equal. Let's denote the length of the hypotenuse of the smaller triangle as $h_s$ , which can be found using the Pythagorean theorem.
$h_s = \sqrt{2^2 + 2^2} = \sqrt{8} = 2\sqrt{2}$
Now we know that the hypotenuse of the smaller triangle is $2\sqrt{2}$ and the hypotenuse of the larger triangle is 5.

STEP 4

Set up the proportion using the hypotenuses of both triangles. The ratio of the hypotenuses should be equal to the ratio of the corresponding sides.
$\frac{2\sqrt{2}}{5} = \frac{2}{y}$

STEP 5

Cross-multiply to solve for $y$ .
$2y = 5 \cdot 2\sqrt{2}$

STEP 6

Simplify the equation to find $y$ .
$2y = 10\sqrt{2}$
Divide both sides by 2:
$y = 5\sqrt{2}$

STEP 7

Verify the solution by checking if the calculated value of $y$ satisfies the given conditions.
The base of the larger triangle is $5\sqrt{2}$ , which is consistent with the proportions given by the similar triangles.
Solution: The length of the base of the larger triangle is $5\sqrt{2}$ .

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Question\begin{align} 2y + 2 &= 5 \\ \end{align}

Studdy Solution

STEP 1

STEP 2

1. Set up a proportion based on the similarity of the triangles.
2. Solve the proportion to find the value of $y$ .
3. Verify the solution by checking if it satisfies the given conditions.

STEP 3

STEP 4

Set up the proportion using the hypotenuses of both triangles. The ratio of the hypotenuses should be equal to the ratio of the corresponding sides.
$\frac{2\sqrt{2}}{5} = \frac{2}{y}$

STEP 5

Cross-multiply to solve for $y$ .
$2y = 5 \cdot 2\sqrt{2}$

STEP 6

Simplify the equation to find $y$ .
$2y = 10\sqrt{2}$
Divide both sides by 2:
$y = 5\sqrt{2}$

STEP 7

Verify the solution by checking if the calculated value of $y$ satisfies the given conditions.
The base of the larger triangle is $5\sqrt{2}$ , which is consistent with the proportions given by the similar triangles.
Solution: The length of the base of the larger triangle is $5\sqrt{2}$ .

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Question\begin{align*} 2y + 2 &= 5 \\ \end{align*}

Studdy Solution

STEP 1

STEP 2

1. Set up a proportion based on the similarity of the triangles.2. Solve the proportion to find the value of yyy.3. Verify the solution by checking if it satisfies the given conditions.

STEP 3

STEP 4

Set up the proportion using the hypotenuses of both triangles. The ratio of the hypotenuses should be equal to the ratio of the corresponding sides.225=2y \frac{2\sqrt{2}}{5} = \frac{2}{y} 522​​=y2​

STEP 5

Cross-multiply to solve for yyy.2y=5⋅22 2y = 5 \cdot 2\sqrt{2} 2y=5⋅22​

STEP 6

Simplify the equation to find yyy.2y=102 2y = 10\sqrt{2} 2y=102​Divide both sides by 2:y=52 y = 5\sqrt{2} y=52​

STEP 7

Verify the solution by checking if the calculated value of yyy satisfies the given conditions.The base of the larger triangle is 525\sqrt{2}52​, which is consistent with the proportions given by the similar triangles. Solution: The length of the base of the larger triangle is 525\sqrt{2}52​.

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Question\begin{align} 2y + 2 &= 5 \\ \end{align}

1. Set up a proportion based on the similarity of the triangles.
2. Solve the proportion to find the value of $y$ .
3. Verify the solution by checking if it satisfies the given conditions.

Set up the proportion using the hypotenuses of both triangles. The ratio of the hypotenuses should be equal to the ratio of the corresponding sides.
$\frac{2\sqrt{2}}{5} = \frac{2}{y}$

Cross-multiply to solve for $y$ .
$2y = 5 \cdot 2\sqrt{2}$

Simplify the equation to find $y$ .
$2y = 10\sqrt{2}$
Divide both sides by 2:
$y = 5\sqrt{2}$

Verify the solution by checking if the calculated value of $y$ satisfies the given conditions.
The base of the larger triangle is $5\sqrt{2}$ , which is consistent with the proportions given by the similar triangles.
Solution: The length of the base of the larger triangle is $5\sqrt{2}$ .