Rectangle has one side 14 cm longer than the other.it's diameter is 34 cm. what are it's dimensions?
Answers
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Given : A rectangle has one side 14cm longer than the other.
It's diagonal is 34cm.
To Find : What are it's dimensions
Solution:
A rectangle has one side 14cm longer than the other.
Let say sides are x , x + 14 cm
Diagonal = 34 cm
Using Pythagorean theorem
x² + (x + 14)² = 34²
=> x² + x² + 28x + 196 = 1156
=> 2x² + 28x - 960 = 0
=> x² + 14x - 480 = 0
=> x² + 30x - 16x - 480 = 0
=> x(x + 30)-16(x + 30) = 0
=> (x - 16) (x + 30) = 0
=> x = 16 or x = - 30
Length can not be negative
Hence x = 16
x + 14 = 30
Hence Dimension of rectangle are 16 , 30
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