Page 147 - Start Up Mathematics_8 (Non CCE)

fi 60t = 50t + 200
fi 60t – 50t = 200 (Transposing 50t to LHS)
fi 10t = 200

10t 200
fi = (Dividing both sides by 10)
10 10
fi t = 20 hours
\ Distance between Delhi and Kolkata = 60 × t = 60 × 20 = 1,200 km
Example 20: Each side of a triangle is increased by 10 cm. If the ratio of the perimeter of the new triangle
to the given triangle is 5 : 4, find the perimeter of the given triangle. (NCERT)
Solution: Let the perimeter of the given triangle be x cm.
If a, b, c are the three sides of the given triangle, then
a + b + c = x ...(1)

Each side is increased by 10 cm.
\ New sides are a + 10, b + 10, c + 10
\ Perimeter of new triangle = (a + 10) + (b + 10) + (c + 10)
= a + b + c + 30 = x + 30 ...(from 1)
Perimeterofnew triangle 5
According to the question, =
Perimeterofgiven triangle 4
x + 30 5
fi = (Cross-multiply)
x 4
fi 5x = 4(x + 30)
fi 5x = 4x + 120
fi 5x – 4x = 120 (Transposing 4x to LHS)
fi x = 120
\ Perimeter of the given triangle is 120 cm.

MATHS LAB ACTIVITY
Objective: To form age relationship in terms of linear equation in one variable
Example: Let your age be 15 years and your teacher’s age be 35 years.
What relationship can you think of between the two ages?
Let’s try...
The obvious relationship is that your teacher’s age is 5 years more than twice your age. In terms of
one variable if, your age = x years your teacher’s age = (2x + 5) years
But you already know that to solve for x, you need two conditions.
The second relationship is that the sum of your ages is 50.
i.e., x + 2x + 5 = 50
fi 3x + 5 = 50
fi 3x = 50 – 5 = 45
45
fi x = = 15
3
Isn’t it fun to form equations using relations!
Repeat this activity and try forming age relationships between you and your:
(a) father (b) mother (c) brother/sister

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