Geometry
posted by Anonymous .
A rectangle has side lengths in the ratio 2:3. The ratio of the rectangles's perimeter to its area is 5:9. What is the length of the longer leg of the rectangle?

Geometry 
Reiny
let the width be 2x and the length be 3x
Area = 6x^2
perimeter = 10
10x/6x^2 = 5/9
30x^2 = 90x
divide by 30 and factor
x(x3) = 0
x = 0 or x = 3, x=0 is not admissable (we have to have some sort of a width)
the width is 6 and the length is 9
check:
area = 54
perimeter = 30
what is 30/54 ??
Respond to this Question
Similar Questions

Geometry
Rectangles The ratio of the length to the width of one rectangle is proportional to the ratio of the length to the width of a smaller rectangle. Describe the circumstances for which this proportion involves a geometric mean. 
math
the lengths of corresponding sides of similar rectangles have a ratio of 7:4 the perimeter of the smaller rectangle is 80 ft. what is the peremiter of the larger rectangle? 
Math
Determine the perimeter and area of a rectangle that has a width of 6 inches and a length of 8 inches. Using a ratio of 1:2, draw a similar rectangle that is double the width and length of the first shape. Determine the perimeter and … 
math
the ratio of the lengths of the corresponding sides of two rectangles is 8:3. The area of the larger rectangle is 320 ft^2. What is the area of the smaller rectangle? 
Math
The first question is this: Helen designs a rectangle with an area of 225 square units. Her rectangle is the largest rectangle (that is, with largest area) with wholenumber side lengths that can be made from the perimeter of the rectangle. … 
Algebra Homework, HELP!
1) A rectangle has an area of 297 square inches and a width which is three inches less than four times the length. Find the length and the width of the rectangle. 2) Let x represent the length of the shorter leg in a right triangle. … 
Algebra, URGENT!!!
1) The first leg of a right triangle is 6 cm longer than its second leg. If the hypotenuse has a length of 8 cm, find the exact lengths of the two legs. First Leg: Second Leg: 2) The length of a rectangle is 10 m longer than its width … 
math
For each of two rectangles, the length to width ratio is 3:2. The ratio of the length of the larger rectangle to the length of the smaller rectangle is 7:5. What is the ratio of the area of the two rectangles? 
Geometry
A diagonal of a square has the same length as a diagonal of a rectangle. The area of the rectangle is 60% of the area of the square. What is the ratio of the shorter side to the longer side of the rectangle? 
math
The lengths of the sides of a rectangle are in a ratio of 4:7. If the length is 31.5 in., find the width, perimeter and area of this rectangle.