Karen, Mary and Amy sold candy bars as a fundraiser. Karen sold three more than twice the number of bars Mary sold. Amy sold fiv
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Answer:
- Value of missing side i.e. TE is <u>1</u><u>2</u><u> </u><u>feet</u>
Step-by-step explanation:
In this question we are provided with a <u>right</u><u> </u><u>angle </u><u>triangle</u> having <u>TS </u><u>-</u><u> </u><u>35</u><u> </u><u>ft </u><u>and</u><u> </u><u>SE </u><u>-</u><u> </u><u>37</u><u> </u><u>ft </u>. And we are asked to find the missing side that is <u>TE </u>using Pythagorean Theorem .
<u>Pythagorean Theorem :</u> -
According to Pythagorean Theorem sum of squares of perpendicular and base is equal to square of hypotenuse in a right angle triangle i.e.
- H² = P² + B²
<u>Where </u><u>,</u>
- H refers to <u>Hypotenuse</u>
- P refers to <u>Perpendicular</u>
- B refers to <u>Base</u>
<u>Solution</u><u> </u><u>:</u><u> </u><u>-</u>
In the given triangle ,
- Base = <u>TE </u>
- Perpendicular = <u>TS </u><u>(</u><u> </u><u>35</u><u> </u><u>feet </u><u>)</u>
- Hypotenuse = <u>SE </u><u>(</u><u> </u><u>37</u><u> </u><u>feet </u><u>)</u>
Now applying Pythagorean Theorem :
Substituting values :
Simplifying it ,
Subtracting 1225 on both sides :
We get ,
Applying square root to both sides :
We get ,
- <u>Henceforth</u><u> </u><u>,</u><u> </u><u>value </u><u>of </u><u>missing </u><u>side </u><u>is </u><em><u>1</u></em><em><u>2</u></em><em><u> </u></em><em><u>feet </u></em><em><u>.</u></em>
<u>Verifying</u><u> </u><u>:</u><u> </u><u>-</u>
Now we are verifying our answer using Pythagorean Theorem . We know that according to Pythagorean Theorem ,
- SE² = TS² + TE²
Substituting value of SE , TS and TE :
- 37² = 35² + <u>1</u><u>2</u><u>²</u>
- 1369 = 1225 + 144
- 1369 = 1369
- L.H.S = R.H.S
- Hence , Verified .
<u>Therefore</u><u> </u><u>,</u><u> </u><u>our</u><u> answer</u><u> is</u><u> correct</u><u> </u><u>.</u>
<h2><u>#</u><u>K</u><u>e</u><u>e</u><u>p</u><u> </u><u>Learning</u></h2>