the length of a rectangle is (x-3) inches long, and the width 3 2/5 inches. If the area is 15 3/10 square inches, write and solve an equation to find the length of the rectangle
(x -3)(3 2/5) = 15 3/10
(x-3) (17/5) = 153/10
(x-3) = (153/10)(5/17)
x-3 = 153/34
x-3 = 4 1/2
x = 7 1/2
To find the length of the rectangle, we can use the formula for the area of a rectangle, which is given by:
Area = Length × Width
Given:
Length = (x - 3) inches
Width = 3 2/5 inches
Area = 15 3/10 square inches
Now we can substitute the given values into the area formula and solve for x.
Area = Length × Width
15 3/10 = (x - 3) × 3 2/5
To simplify the equation, we can convert the mixed numbers to improper fractions:
15 3/10 = (x - 3) × (17/5)
Next, we can multiply both sides of the equation by 10 to eliminate the fractions:
15 3/10 × 10 = (17/5) × (x - 3) × 10
The left side simplifies to 153/10:
153/10 = (17/5) × (x - 3)
Now, we can multiply the fractions:
153/10 = 17/5 × (x - 3)
To simplify the equation further, we can cancel out common factors:
153/10 = (17/1) × (x - 3)
153/10 = 17(x - 3)
Next, we can solve for x by isolating it:
2(x - 3) = 153/10
2x - 6 = 153/10
Multiply both sides of the equation by 10 to eliminate the fraction:
20x - 60 = 153
Add 60 to both sides:
20x = 213
Divide both sides by 20 to solve for x:
x = 213/20
So, the length of the rectangle is x = 213/20 inches.