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# math

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a right angled triangle has short side of 6 cm and long side of 18 cm. find the middle side of the triangle

Guest Oct 19, 2017

#3
+302
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My interpretation: The shortest side of the right triangle is 6cm and the hypotenuse is 18cm.

Pythagorean Theorem: $$leg1^2+leg2^2=hyp^2$$

$$6^2+?^2=18^2$$

$$36+?^2=324$$

$$?^2=288$$

$$?=\sqrt{288}$$

Simplifying, we get $$?=12\sqrt{2}$$ cm.

Mathhemathh  Oct 20, 2017
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#1
+84129
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The remaining side will be given by :

sqrt ( 18^2 - 6^2 )  = sqrt (288)  =  sqrt (144 * 2)  =  sqrt (144) * sqrt (2)  =  12sqrt(2)  cm  ≈

16.97 cm

CPhill  Oct 19, 2017
#2
+394
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If the triangle has a right angle then that means that two sides are identical. So if the short side is 6cm, and the longer side is 18cm then the middle side will be 6cm as well. If the long side is 18cm then the middle side will be:

SOLUTION: 6cm

Mr.Owl  Oct 19, 2017
edited by Mr.Owl  Oct 19, 2017
#3
+302
+2

My interpretation: The shortest side of the right triangle is 6cm and the hypotenuse is 18cm.

Pythagorean Theorem: $$leg1^2+leg2^2=hyp^2$$

$$6^2+?^2=18^2$$

$$36+?^2=324$$

$$?^2=288$$

$$?=\sqrt{288}$$

Simplifying, we get $$?=12\sqrt{2}$$ cm.

Mathhemathh  Oct 20, 2017

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