Which Set of Numbers Can Represent the Side Lengths, in Inches, of an Acute Triangle?

The set of number which represent the length of the sides of an acute triangle is $5,7,8$ i.due east., $\fbox{\begin\\\ \bf option 2\\\end{minispace}}$ .

Further caption:

A triangle is two dimensional figure which is formed when three non-collinear points are joined. It has three sides, three angles and three edges.

Consider a triangle with sides as $L_{1},L_{2} \text{and} L_{3}$ such that $L_{3}>L_{2}>L_{1}$ .

The categorization of a triangle on the basis of side is as follows:

one) Acute triangle: If the square of the longest side is smaller than the sum of the square of the other two sides than the triangle is an acute triangle.

This implies that if, $(L_{3})^{2}$ then the triangle is an acute triangle.

2) Obtuse triangle: If the square of the longest side is greater than the sum of the square of the other two sides than the triangle is an birdbrained triangle.

This implies that if, $(L_{3})^{2}>(L_{1})^{2}+(L_{2})^{2}$ so the triangle is an birdbrained triangle.

3) Right triangle:

If the foursquare of the longest side is equal to the sum of the square of the other two sides than the triangle is a correct triangle.

This implies that if, $(L_{3})^{2}=(L_{1})^{2}+(L_{2})^{2}$ so the triangle is a right triangle.

Option1:

In option i it is given that the length of the sides of the triangle are $L_{1}=4$ , $L_{2}=5$ and $L_{3}=7$ .

The length of the longest side is $7$ units.

The foursquare of the length of the longest side is calculated as follows:

$(L_{3})^{2}=49$

Calculate the value of $(L_{1})^{2}+(L_{2})^{2}$ as follows:

$\begin{aligned}(L_{1})^{2}+(L_{2})^{2}&=16+25\\&=41\end{aligned}$

This implies that for selection i the square of the length of the longest side is greater than the sum of the squares of the other two sides. And so, the triangle with sides $L_{1}=4$ , $L_{2}=5$ and $L_{3}=7$ is an birdbrained triangle.

Therefore, the pick 1 is incorrect.

Option2:

In option 2 it is given that the length of the sides of the triangle are $L_{1}=5$ , $L_{2}=7$ and $L_{3}=8$ .

The length of the longest side is $8$ units.

The square of the length of the longest side is calculated as follows:

$(L_{3})^{2}=64$

Calculate the value of $(L_{1})^{2}+(L_{2})^{2}$ as follows

$\begin{aligned}(L_{1})^{2}+(L_{2})^{2}&=25+49\\&=74\end{aligned}$

This implies that for option ii the square of the length of the longest side is smaller than the sum of the squares of the other two sides. And so, the triangle with the side $L_{1}=5$ , $L_{2}=7$ and $L_{3}=8$ is an acute triangle.

Therefore, the pick 2 is correct.

Option3:

In choice three it is given that the length of the sides of the triangle are $L_{1}=6$ , $L_{2}=7$ and $L_{3}=10$ .

The length of the longest side is $10$ units.

The square of the length of the longest side is calculated as follows:

$(L_{3})^{2}=100$

Summate the value of $(L_{1})^{2}+(L_{2}){2}$ as follows:

$\begin{aligned}(L_{1})^{2}+(L_{2})^{2}&=36+49\\&=85\end{aligned}$

This implies that for option 3 the square of the length of the largest side is greater than the sum of the squares of the other two sides. So, the triangle with the side $L_{1}=6$ , $L_{2}=7$ and $L_{3}=10$ is an birdbrained triangle.

Therefore, the option iii is wrong.

Option4:

In option four it is given that the length of the sides of the triangle are $L_{1}=7$ , $L_{2}=9$ and $L_{3}=12$ .

The length of the longest side is $12$ units.

The square of the length of the longest side is calculated every bit follows:

$(L_{3})^{2}=144$

Calculate the value of $(L_{1})^{2}+(L_{2})^{2}$ as follows:

$\begin{aligned}(L_{1})^{2}+(L_{2})^{2}&=49+81\\&=130\end{aligned}$

This implies that for option four the square of the length of the largest side is greater than the sum of the squares of the other two sides. So, the triangle with the side $L_{1}=7$ , $L_{2}=9$ and $L_{3}=12$ is an

obtuse triangle.

Therefore, the option 4 is incorrect.

Thus, the ready of number which represent the length of the sides of an acute triangle is $5,7,8$ i.e., $\fbox{\begin\\\ \bf option 2\\\end{minispace}}$ .

Learn more:

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2. A problem to make up one's mind the slope intercept form of a line brainly.com/question/1473992

3. Changed function brainly.com/question/1632445

Respond details

Grade: High schoolhouse

Subject: Mathematics

Chapter: Triangles

Keywords: Geometry, triangles, acute triangle, obtuse triangles, right triangle, longest side, sum of longest side, classification of triangle, not-collinear points, 90 degrees, 5,vii,eight.

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Source: https://brainly.com/question/2125469

Which Set of Numbers Can Represent the Side Lengths, in Inches, of an Acute Triangle?

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