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?
1 answer:
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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