Asked by Gilda
Application of Quadratic Equations
The base of a triangle is longer than twice its corresponding height by 1 cm. The area of the triangle is 105 cm(square). Find the height of the triangle
The base of a triangle is longer than twice its corresponding height by 1 cm. The area of the triangle is 105 cm(square). Find the height of the triangle
Answers
Answered by
Reiny
height ---- x
base ---- 2x + 1
(1/2)(base)(height) = area
(1/2)(2x+1)(x) = 105
x(2x+1) = 210
2x^2 + x - 210 = 0
(x-10)(2x+21) = 0
x = 10 or x = -21/2 , but obviously x has to be positive, so
x = 10
The height is 10 cm
check:
height is 10
base is 21
area = (1/2)(21)(10) = 105
answer is correct
base ---- 2x + 1
(1/2)(base)(height) = area
(1/2)(2x+1)(x) = 105
x(2x+1) = 210
2x^2 + x - 210 = 0
(x-10)(2x+21) = 0
x = 10 or x = -21/2 , but obviously x has to be positive, so
x = 10
The height is 10 cm
check:
height is 10
base is 21
area = (1/2)(21)(10) = 105
answer is correct
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