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The length of a diagonal of a rectangular park is 40 meters, and that of one of its sides is 24 meters. Find the perimeter of the park.
102 m
112 m
122 m
132 m
112 m
Recognize the Pythagorean triple (3, 4, 5). Here, 40=5├Ч8 and 24=3├Ч8, so the missing side is 4├Ч8=32. Perimeter = 2(24+32)=112.
Diagonal (d) = 40 m, Length (l) = 24 m
d2=l2+b2, P=2(l+b)
Recognize the Pythagorean triple (3, 4, 5). Here, 40=5├Ч8 and 24=3├Ч8, so the missing side is 4├Ч8=32. Perimeter = 2(24+32)=112.
Students often misidentify the diagonal as one of the sides or calculate the area (l├Чb) instead of the perimeter (2(l+b)).
Calculate the unknown side (b)
Since the park is rectangular, the diagonal forms a right-angled triangle. By Pythagoras theorem, the width b is d2тИТl2тАЛ.
b=402тИТ242тАЛ=1600тИТ576тАЛ=1024тАЛ=32┬аm
Calculate the perimeter (P)
Substitute the length l=24 and width b=32 into the perimeter formula P=2(l+b).
P=2(24+32)=2(56)=112┬аm
B is correct because the calculated perimeter of the rectangular park is 112 m.
Pythagorean triples are vital for Geometry; memorizing common sets like (3,4,5), (5,12,13), and (8,15,17) significantly speeds up Coordinate Geometry and Mensuration problems.
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