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inna [77]
3 years ago
6

Leonardo decided to start training to run in a marathon to keep in shape. After 5 training sessions, he had run a total of 25 mi

les. Leo decided to take it easy at his training session today and only run half his normal distance. How far did he run? *
Mathematics
1 answer:
lisov135 [29]3 years ago
8 0
Total distance ran by Leonardo in 5 training sessions = 25 miles
Then
Total distance ran by Leonardo in 1 training session = (25/5) miles
                                                                                   = 5 miles
Total distance ran by Leonardo today was half the distance he actually covers in every training session.
So
Total distance ran by Leonardo today = (5/2) miles
                                                             = 2.5 miles
So Leonardo ran for a distance of 2.5 miles today. <span>It is actually very important to read the question carefully and then the answering the question becomes easy.

</span>



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Each leg of a 45°-45°-90° triangle measures 12 cm. Triangle X Y Z is shown. Angle X Y Z is a right angle and angles Y Z X and Z
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Answer:

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Step-by-step explanation:

We are given with a right angled triangle which has angles 45°-45°-90° and sides as 12 cm each.

Following labeling of dimensions is provided:

\angle XYZ = 90^\circ\\\angle YZX = 45^\circ\\\angle ZXY = 45^\circ

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Please refer to the image attached as well.

<u>To find: </u> The hypotenuse, XZ = ?

It is well known that if the triangle is a right angled triangle, the pythagorean theorem holds well. As per the theorem:

\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Height}^{2}\\

Here, Base is ZY = 12 cm

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Putting the values:

XZ^2=12^2+12^2\\\Rightarrow XZ^2=144+144\\\Rightarrow XZ=\sqrt{144+144}\\\Rightarrow XZ=\sqrt{288}\\\Rightarrow XZ=12\sqrt{2}\ cm

So, the answer is <em>Hypotenuse, XZ = </em>12\sqrt{2}\ cm<em>.</em>

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