Question #e9576

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Answer 1 · 2018-01-11T04:09:52

$x = 51.72 meters$ $color(red)"x = 51.72 meters"$

$y = 108.28 meters$ $color(blue)"y = 108.28 meters"$

Data

$x + y = 160 meters$ $"x + y = 160 meters"$

Sides form a triangle 📐 , so

$x^{2} + y^{2} = {(120)}^{2}$ $x^2 + y^2 = (120)^2$

Combining equations:

$x^{2} + (160 - x^{2}) = {(120)}^{2}$ $x^2 + (160 - x^2) = (120)^2$

Re-arranging:

$x^{2} - 160 x^{2} + 5600 = 0$ $x^2 - 160x^2 + 5600 = 0$

Solving quadratic equation:

$x = 160 \pm \frac{\sqrt{(160^{2} - 4 (5600))}}{2}$ $x = 160 +-sqrt((160^2- 4(5600)))/2$

$x = \frac{160 \pm 56.57}{2}$ $x = (160 +-56.57)/2$