The length of a diagonal of a rectangle is 85 cm. When length of its shortest side is increased by 11 cm and that of longest side is decreased by 7 cm. the length of the diagonal remains same. Find the length and breadth of the rectangle.
Answers
Answer:
75 & 40 cm
Step-by-step explanation:
The length of a diagonal of a rectangle is 85 cm. When length of its shortest side is increased by 11 cm and that of longest side is decreased by 7 cm. the length of the diagonal remains same. Find the length and breadth of the rectangle.
Let say Length & Breadth of Rectangle are L & B cm L > B
Diagonal = √(L² + B²)
=> 85 = √(L² + B²)
=> 85² = L² + B²
(L - 7)² + (B + 11)² = 85²
L² + 49 - 14L + B² + 121 +22B = 7225
=> L² + B² -14L + 22B = 7055
=> 7225 + 22B - 14L = 7055
=> 22B - 14L = -170
=> 11B - 7L = -85
=> 7L = 11B + 85
=> L = (11B + 85)/7
putting in 85² = L² + B²
=> ((11B + 85)/7 )² + B² = 85²
=> 121B² + 85² + 22B*85 + 49B² = 49*85²
=> 170B² + 22*85B - 48*85² = 0
=> 2B² + 22B - 48*85 = 0
=> B² + 11B - 24*85 = 0
=> B² + 51B - 40B - 24*85 =0
=> B(B + 51) - 40(B + 51) = 0
=> B = 40
& L = (11B + 85)/7 = (11*40 + 85)/7 = 75
length and breadth of the rectangle 75 & 40 cm