Subtract the sides

Geometry Level 2

A hypotenuse of a right triangle is c = 20 c = 20 and the area of the triangle is 100 100 .

If the other two sides are a a and b b , find the value of ∣ a − b ∣ \left| a - b \right| .


The answer is 0.

Milan Milanic by Milan Milanic , 24, Serbia

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2 solutions

Rishabh Jain
Jan 22, 2016

G i v e n : a 2 + b 2 = c 2 = 400 a n d 2 × a b = 4 × A r e a = 400 \small{\color{#3D99F6}{Given:}~a^2+b^2=c^2=400~and ~2\times ab=4\times Area=400} ∣ a − b ∣ = a 2 + b 2 − 2 a b = 400 − 400 |a-b|=\sqrt{a^2+b^2-2ab}=\sqrt{400-400} = 0 \Large ~~~~~~~~~~~~~~~~=0

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Milan Milanic
Jan 22, 2016

Solution:

Area: 100 = c × h c 2 ⇒ h c = 10 100 = \frac{c \times h_{c}}{2} \Rightarrow h_{c} = 10 .

Since, h c = c 2 h_{c} = \frac{c}{2} right triangle is also an isosceles one, meaning a = b a = b .

Solution: 0 \boxed{0} .

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