Given square ABCD with diagonals AC, BD.If DB = 7x + 1 and AE = 2x + 11, find EB.
Accepted Solution
A:
Answer: The length of EB is 25 unit Step-by-step explanation:Given as: ABCD is a square With diagonal AC and BD The length of DB = 7x + 1 The length of AE = 2x + 11The mid point of BD and AC is ELet the each side of square be m So, BD² = m² + m² Or, (7x + 1) = 2 m² Or m² = [tex]\frac{(7x + 1)}{2}[/tex] Again AC² = m² + m² = 2 m²Or, AC = (7x + 1) ∵ AE is the half of diagonal AC So, AE = [tex]\frac{1}{2}[/tex] × (7x + 1) Or, 2x + 11 = [tex]\frac{1}{2}[/tex] × (7x + 1) or , 4x + 22 = 7x + 1Or, 3x = 21 ∴ x = 7 unitSo, BD = 7 (7 ) + 1 = 50 unitSo, BE is the half of diagonal BD Or, BE = [tex]\frac{1}{2}[/tex] × 50 = 25 unitHence The length of EB is 25 unit Answer