The diagonal of a rectangular field is 60 metres more than the shorter side. If the
longer side is 30 metres more than the shorter side: Find the sides of the field.
Answers
Given data :
- The diagonal of a rectangular field is 60 metres more than the shorter side.
- If the longer side is 30 metres more than the shorter side.
To find : The sides of the field ?
Solution : Let, shorter side of the rectangular field be its breadth. and the longer side of the rectangular field be its length.
where,
- lenght = L
- breadth = B
- diagonal = D
Now, according to given,
→ D = B + 60 ......( 1 ) and
→ L = B + 30 ......( 2 )
We know that, by property of rectangle : All angles of rectangle are equal to 90°.
Now, by pythagoras theorem :
→ (hypotenuse)² = (1.st side)² + (2.cd side)²
→ ( D )² = ( L )² + ( B )²
{from eq. ( 1 ) and eq. ( 2 )}
→ ( B + 60 )² = ( B + 30 )² + B²
→ B² + 120B + 3600 = B² + 60B + 900 + B²
→ B² + 120B + 3600 = 2B² + 60B + 900
→ B² - 2B² + 120B - 60B + 3600 - 900 = 0
→ - B² + 60B + 2700 = 0. i.e.
→ B² - 60B - 2700 = 0
→ B² - 90B + 30B - 2700 = 0
→ B * ( B - 90 ) + 30 * ( B - 90 ) = 0
→ ( B + 30 ) ( B - 90 ) = 0
→ B + 30 = 0 or B - 90 = 0
→ B = - 30 or B = 90
Here, we know that breadth of rectangular field is never negative.
∴ B ≠ - 30 and B = 90 metre
Now, put value of B in eq. ( 2 )
→ L = B + 30
→ L = 90 + 30
→ L = 120 metre
Answer : Hence, the sides of the rectangular field are 120 metre and 90 metre respectively. {length = 120 metre and breadth = 90 metre}
Verification :
→ ( B + 60 )² = ( B + 30 )² + B²
→ ( 90 + 60 )² = ( 90 + 30 )² + 90²
→ 150² = 120² + 90²
→ 22500 = 14400 + 8100
→ 22500 = 22500
Hence, verified.
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