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In a certain isosceles right triangle, the altitude to the hypotenuse has length $4\sqrt{2}$. What is the area of the triangle?

 Oct 26, 2019
 #1
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Right isosceles triangle.

Sides: a = 8   b = 8   c = 11.314

Area: T = 32
Perimeter: p = 27.314
Semiperimeter: s = 13.657

Angle ∠ A = α = 45° = 0.785 rad
Angle ∠ B = β = 45° = 0.785 rad
Angle ∠ C = γ = 90° = 1.571 rad

Height: ha = 8
Height: hb = 8
Height: hc = 5.657

 Oct 26, 2019
 #2
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+1

Here is a formula :


A = x^2

 

Where x represents the distance from altitude to the hypotenuse.

 

In this case it is \(4\sqrt{2}\).

 


So the area is 32

CalculatorUser  Oct 26, 2019
edited by CalculatorUser  Oct 26, 2019
 #3
avatar+2417 
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I believe guest proved the formula

CalculatorUser  Oct 26, 2019

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