The side of a square exceeds the side of another square by 4 cm and the sum of the areas of the two squares is 400 sq. cm. Find the dimensions of the squares.
OR
A fast train takes 3 hours less than a slow train for a journey of 600 km. If the speed of the slow train is 10 km/hour less than that of the fast train, find the speeds of the two trains.
Answers
Answer:
12 & 16 cm
50 & 40 km/Hr
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Step-by-step explanation:
Let Side of 1st square = x cm
Then side of 2nd square = x + 4 cm
Area of 1st = x²
Area of 2nd = (x+4)²
x² + (x+4)² = 400
x² + x² + 16 + 8x = 400
2x² + 8x - 384 = 0
x² + 4x - 192 = 0
x² + 16x - 12x - 192 = 0
(x+16)(x-12) = 0
so x = 12 as it can not be negative
dimensions of 1st square = 12 cm each side
dimension of 2nd square = 12+4 = 16 cm each side
Question 2
Fast train speed = F km/hr
Slow speed train = F-10 km/hr
Time take by fast train = 600/F
Time taken by slow time = 600/(F-10)
600/(F-10) - 600/F = 3
600(F - (F-10)) = 3F(F-10)
6000 = 3F² - 30F
F² - 10F - 2000 = 0
F² - 50F + 40F-600 = 0
(F-50)(F+40) = 0
F = 50 ( as F can not be -40)
Speed of fast train = 50 km/hr
Speed of slow train = 50-10 = 40 km/hr