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applying the acute triangle inequality theorem try it use the drop-down…

$4^2$ is $\boldsymbol{<}$ $3^2 + 3^2$. Therefore, $\triangle JKL$ is $\boldsymbol{\text{an acute triangle}}$. $5^2$ is $\boldsymbol{=}$ $3^2 + 4^2$. Applying the same method, $\tr…

Catégorie: geometry Mis à jour: 2026-02-09

Question

applying the acute triangle inequality theorem
try it
use the drop-down menus to complete the statements.
$4^2$ is $\boldsymbol{vee}$ $3^2 + 3^2$.
therefore, $\\triangle jkl$ is $\boldsymbol{vee}$.
$5^2$ is $\boldsymbol{vee}$ $3^2 + 4^2$.
applying the same method, $\\triangle abc$ is $\boldsymbol{vee}$.
(there are two triangles: $\\triangle abc$ with side lengths $ac=3$, $bc=4$, $ab=5$; $\\triangle jkl$ with side lengths $jk=3$, $kl=3$, $jl=4$)

Étapes de solution

  1. Understand the question

    applying the acute triangle inequality theorem
    try it
    use the drop-down menus to complete the statements.
    $4^2$ is $\boldsymbol{vee}$ $3^2 + 3^2$.
    therefore, $\\triangle jkl$ is $\boldsymbol{vee}$.
    $5^2$ is $\boldsymbol{vee}$ $3^2 + 4^2$.
    applying the same method, $\\triangle abc$ is $\boldsymbol{vee}$.
    (there are two triangles: $\\triangle abc$ with side lengths $ac=3$, $bc=4$, $ab=5$; $\\triangle jkl$ with side lengths $jk=3$, $kl=3$, $jl=4$)

  2. Explanation

    Step1: Calculate $4^2$, $3^2+3^2$

    $4^2=16$, $3^2+3^2=9+9=18$

    Step2: Compare $4^2$ and $3^2+3^2$

    $16 < 18$, so $4^2 < 3^2+3^2$

    Step3: Classify $\triangle JKL$

    Since the square of the longest side is less than the sum of squares of the other two sides, $\triangle JKL$ is acute.

    Step4: Calculate $5^2$, $3^2+4^2$

    $5^2=25$, $3^2+4^2=9+16=25$

    Step5: Compare $5^2$ and $3^2+4^2$

    $25 = 25$, so $5^2 = 3^2+4^2$

    Step6: Classify $\triangle ABC$

    Since the square of the longest side equals the sum of squares of the other two sides, $\triangle ABC$ is right.

  3. Final answer

    $4^2$ is $\boldsymbol{<}$ $3^2 + 3^2$.
    Therefore, $\triangle JKL$ is $\boldsymbol{\text{an acute triangle}}$.
    $5^2$ is $\boldsymbol{=}$ $3^2 + 4^2$.
    Applying the same method, $\triangle ABC$ is $\boldsymbol{\text{a right triangle}}$.

Réponse

Explanation

Step1: Calculate $4^2$, $3^2+3^2$

$4^2=16$, $3^2+3^2=9+9=18$

Step2: Compare $4^2$ and $3^2+3^2$

$16 < 18$, so $4^2 < 3^2+3^2$

Step3: Classify $\triangle JKL$

Since the square of the longest side is less than the sum of squares of the other two sides, $\triangle JKL$ is acute.

Step4: Calculate $5^2$, $3^2+4^2$

$5^2=25$, $3^2+4^2=9+16=25$

Step5: Compare $5^2$ and $3^2+4^2$

$25 = 25$, so $5^2 = 3^2+4^2$

Step6: Classify $\triangle ABC$

Since the square of the longest side equals the sum of squares of the other two sides, $\triangle ABC$ is right.

Answer

$4^2$ is $\boldsymbol{<}$ $3^2 + 3^2$.
Therefore, $\triangle JKL$ is $\boldsymbol{\text{an acute triangle}}$.
$5^2$ is $\boldsymbol{=}$ $3^2 + 4^2$.
Applying the same method, $\triangle ABC$ is $\boldsymbol{\text{a right triangle}}$.

Question Image

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Question Analysis

Subject mathematics
Sub Subject geometry
Education Level high school
Difficulty unspecified
Question Type with image, calculation
Multi Question No
Question Count 1
Analysis Status completed
Analyzed At 2026-02-09T20:03:27

OCR Text

Show OCR extraction 
applying the acute triangle inequality theorem
try it
use the drop-down menus to complete the statements.
$4^2$ is $\boldsymbol{vee}$ $3^2 + 3^2$.
therefore, $\\triangle jkl$ is $\boldsymbol{vee}$.
$5^2$ is $\boldsymbol{vee}$ $3^2 + 4^2$.
applying the same method, $\\triangle abc$ is $\boldsymbol{vee}$.
(there are two triangles: $\\triangle abc$ with side lengths $ac=3$, $bc=4$, $ab=5$; $\\triangle jkl$ with side lengths $jk=3$, $kl=3$, $jl=4$)

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mathematicsgeometrywith image, calculationhigh schoolturns-1

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