Se diseña un patio cuadrado cuya diagonal es 6 metros mayor que la medida de la base ¿cuales son las dimensiones del patio?
Segúnla imagen
<img src="https://tex.z-dn.net/?f=%20%28x%2B6%29%5E%7B2%7D%3D%20%20x%5E%7B2%7D%20%2B%20x%5E%7B2%7D%20" />
<img src="https://tex.z-dn.net/?f=x%5E2%2B12x%2B36%3D2x%5E2" />
<img src="https://tex.z-dn.net/?f=-x%5E2%2B12x%2B36%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%3D-1%2C%5C%3Ab%3D12%2C%5C%3Ac%3D36%3A%5Cquad%20x_%7B1%2C%5C%3A2%7D%3D%5Cfrac%7B-12%5Cpm%20%5Csqrt%7B12%5E2-4%5Cleft%28-1%5Cright%2936%7D%7D%7B2%5Cleft%28-1%5Cright%29%7D" />
<img src="https://tex.z-dn.net/?f=x_%7B1%7D%3D%3D%5Cfrac%7B-12%2B%5Csqrt%7B12%5E2-%5Cleft%28-1%5Cright%29%5Ccdot%20%5C%3A4%5Ccdot%20%5C%3A36%7D%7D%7B-2%7D" />
<img src="https://tex.z-dn.net/?f=x_%7B1%7D%3D%5Cfrac%7B%5Csqrt%7B288%7D-12%7D%7B2%7D%0A%0A%0Ax_%7B1%7D%3D-2%2C49" />
<img src="https://tex.z-dn.net/?f=x_%7B2%7D%3D%3D%5Cfrac%7B-12-%5Csqrt%7B12%5E2-4%5Cleft%28-1%5Cright%29%5Ccdot%20%5C%3A36%7D%7D%7B-2%5Ccdot%20%5C%3A1%7D" />
<img src="https://tex.z-dn.net/?f=x_%7B2%7D%3D%5Cfrac%7B-12-%5Csqrt%7B288%7D%7D%7B-2%7D" />
[img = 10]
Respuesta
Cada lado del patio mide 14, 49 metros.