area of a rright triangular park is 420m^2 whose altitude exceeds base by 11m length of base of triangle and length of altitude and length of longest side of triangular park and length of longest altitude of triangle is
Answers
Given : area of a right triangular park is 420m² whose altitude exceeds base by 11 m length of base of triangle
To Find : length of altitude
length of longest side of triangular park
length of longest altitude of triangle
Solution:
Base = x m
altitude = x + 11 m
Area = (1/2) * base * altitude
= (1/2) * x (x + 11)
(1/2) * x (x + 11) = 420
=> x² + 11x = 840
=> x² + 11x - 840 = 0
=> x² + 35x - 24x - 840 =0
=> (x + 35)(x - 24) = 0
=> x = 24
Base = 24 m
Altitude = 35 m
Hypotenuse² = Base² + Altitude²
=> Hypotenuse² = 24² + 35²
=> Hypotenuse = 42.44 m
length of altitude = 35 m
length of longest side of triangular park = 42.44 m
length of longest altitude of triangle 35 m
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