The longer side of a rectangle is 4meters more than the shorter side. If the area of the rectangle is 60 square meters, then what are the dimensions of the rectangle?
x^2+4x-60=0
(x+10)(x-6)=0
x-6=0 6+4=10
x=6
The shortest is 6m
The longer side is 10m
2. The top of a 15-foot ladder is 3 feet farther up a wall than the foot is from the bottom of the wall. How far is the ladder from the bottom of the wall?
2x^2+6x+9=225
2x^2+6x+9-225=0
2x^2+6x-216=0
x^2+3x-108=0
x=(-3+21)/2=9
x=(-3-21)/2=-12
Answers
Step-by-step explanation:
The longer side of a rectangle is 4meters more than the shorter side. If the area of the rectangle is 60 square meters, then what are the dimensions of the rectangle?
x^2+4x-60=0
(x+10)(x-6)=0
x-6=0 6+4=10
x=6
The shortest is 6m
The longer side is 10m
2. The top of a 15-foot ladder is 3 feet farther up a wall than the foot is from the bottom of the wall. How far is the ladder from the bottom of the wall?
2x^2+6x+9=225
2x^2+6x+9-225=0
2x^2+6x-216=0
x^2+3x-108=0
x=(-3+21)/2=9
x=(-3-21)/2=-12
Given : The longer side of a rectangle is 4 meters more than the shorter side. If the area of the rectangle is 60 square meters,
To Find : the dimensions of the rectangle?
Solution:
Shorter side of Rectangle = x m
Longer side of rectangle = x + 4 m
Area of rectangle = x(x + 4) = 60
=> x² + 4x - 60 = 0
Using middle term split
=> x² + 10x - 6x - 60 =0
=> x(x + 10) - 6(x + 10) =0
=> (x + 10)(x - 6) = 0
=> x = -10 , x = 6
Length can not be negative
Hence x = 6
x + 4 = 6 + 4 = 10
Hence Dimensions of rectangle are 6m and 10 m
The top of a 15-foot ladder is 3 feet farther up a wall than the foot is from the bottom of the wall.
foot is from the bottom of the wall. = x feet
3 feet farther up a wall = x + 3 feet
Using Pythagorean theorem
x² + (x + 3)² = 15²
=> x² + x² + 6x + 9 = 225
=> 2x² + 6x - 216 = 0
=> x² + 3x - 108 = 0
=> x² + 12x - 9x - 108 = 0
=> (x + 12)(x - 9) = 0
=> x = - 12 , x = 9
Distance can not be negative
hence x = 9
the ladder from the bottom of the wall = 9 feet
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