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-BARSIC- [3]
3 years ago
5

Jacinto está cercando un terreno de forma rectangular. Cuando lleva puesto alambre a dos lados consecutivos de la tierra, se da

cuenta que ha gastado 170 m de alambre. Si sabe que la diagonal del rectángulo mide 130 m, ¿cuáles son las dimensiones y el área del terreno?
Mathematics
1 answer:
qwelly [4]3 years ago
4 0

Answer:

Step-by-step explanation:

Given the perimeter of the rectangular shape = 170m

Length of the diagonal = 130m

Perimeter = 2L + 2W

diagonal d² = L² + w²

L is the length of the terrain

w is the width

140 = 2L + 2W

70 = L+W ..... 1

130² = L²+w² ..... 2

from 1, L = 70-w

substitute into 2;

130² = (70-w)²+w²

130² = 4900-140w + 2w²

16900 = 4900-140w + 2w²

2w²-140w - 12000 = 0

w²-70w - 6000 = 0

On factorizing;

(w+50)(w−120) = 0

w - 120 = 0

w = 120 m

Since L = 70 - w

L = 70 - 120

L = -50m

Hence the dimension is 120m by 50 m

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