a triangluar garden has an area of 189 square feet. its height os 3 feet more than ots base. find the measure of the base.

Answer 1

base ---- x
height ---- x+3

(1/2)x(x+3) = 189
x^2 + 3x = 378
x^2 + 3x - 378 = 0
(x-18)(x+21) = 0
x=18 or x=-21, but x can't be negative, so

x=18
base is 18, height is 21

check:area = (1/2)(18x21) = 189

Answer 2

A = Area

b = base

h = height

h = b + 3

A = b * h / 2 = 189 ft ^ 2

b * h / 2 = b * ( b + 3 ) / 2 = 189 Multiply both sides by 2

b * ( b + 3 ) = 378

b ^ 2 + 3 b - 378 = 0

The solutions are :

b = 18 ft

and

b = - 21 ft

The base can't be negative,so solution are :

b = 18 ft

h = b + 3 = 21 ft

Proof :

A = b * h / 2 = ( 18 * 21 ) / 2 = 378 / 2 = 189 ft ^ 2

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b ^ 2 + 3 b - 378 = 0

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b ^ 2 + 3 b - 378 = 0

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