El área de un triángulo mide 117 metros cuadrados y su base supera en un centímetro a los dos tercios de la altura?

El área de un triángulo mide 117 metros cuadrados y su base supera en un centímetro a los dos tercios de la altura.

Calcula la longitud de la base y la de la altura.

AΔ = Base * Altura / 2

<img src="https://tex.z-dn.net/?f=117%3D%5C%3A%5Cfrac%7B%5Cleft%28%5C%3A%5Cfrac%7B2%7D%7B3%7Dx%5C%3A%2B0.01%5Cright%29%5C%3A%5Cleft%28x%5Cright%29%5C%3A%7D%7B2%7D%0A" />

<img src="https://tex.z-dn.net/?f=117%5Ccdot%20%5C%3A2%3D%5Cfrac%7B%5Cleft%28%5Cfrac%7B2%7D%7B3%7Dx%2B0.01%5Cright%29x%7D%7B2%7D%5Ccdot%20%5C%3A2" />

<img src="https://tex.z-dn.net/?f=234%3Dx%5Cleft%28%5Cfrac%7B2%7D%7B3%7Dx%2B0.01%5Cright%29" />

<img src="https://tex.z-dn.net/?f=0.66667%5Cdots%20x%5E2%2B0.01x-234%3D0" />

<img src="https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D0%5Cmathrm%7B%5C%3Alas%5C%3Asoluciones%5C%3Ason%5C%3A%7D" />

<img src="https://tex.z-dn.net/?f=x_%7B1%2C%5C%3A2%7D%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D" />

<img src="https://tex.z-dn.net/?f=%5Cmathrm%7BPara%5C%3A%7D%5Cquad%20a%3D0.66667%5Cdots%20%2C%5C%3Ab%3D0.01%2C%5C%3Ac%3D-234%3A" />

<img src="https://tex.z-dn.net/?f=x_%7B1%2C%5C%3A2%7D%3D%5Cfrac%7B-0.01%5Cpm%20%5Csqrt%7B0.01%5E2-4%5Ccdot%20%5C%3A0.66667%5Cdots%20%5Cleft%28-234%5Cright%29%7D%7D%7B2%5Ccdot%20%5C%3A0.66667%5Cdots%20%7D" />

<img src="https://tex.z-dn.net/?f=x_%7B1%7D%3D%5Cfrac%7B-0.01%2B%5Csqrt%7B0.01%5E2-4%5Ccdot%20%5C%3A0.66667%5Cdots%20%5Cleft%28-234%5Cright%29%7D%7D%7B2%5Ccdot%20%5C%3A0.66667%5Cdots%20%7D%3D%5Cfrac%7B-0.01%2B%5Csqrt%7B624.0001%7D%7D%7B1.33333%5Cdots%20%7D%3D18.7275" />

<img src="https://tex.z-dn.net/?f=x_%7B2%7D%3D%5Cfrac%7B-0.01-%5Csqrt%7B0.01%5E2-4%5Ccdot%20%5C%3A0.66667%5Cdots%20%5Cleft%28-234%5Cright%29%7D%7D%7B2%5Ccdot%20%5C%3A0.66667%5Cdots%20%7D%3D%5Cfrac%7B-0.01-%5Csqrt%7B624.0001%7D%7D%7B1.33333%5Cdots%20%7D%3D-18.7275" />

Remplazar x

Base ⇒ 2 / 3 x + 0.

01

[img = 10]

[img = 11]

Altura⇒ x⇒18.

7275 m.