Question

In: Math

The area of a particular rectangle is 12 times the area of a certain square, and...

The area of a particular rectangle is 12 times the area of a certain square, and the width of the rectangle is three times the length of a side of the square. The perimeter of the rectangle is 30 units greater than the perimeter of the square. Find the dimensiuons of both the rectangle and the square.

Solutions

Expert Solution

here, width of the rectangle is three times the length of a side of the square so,

let represent the width of the rectangle, then represents the length of the side of the square

the perimeter of the rectangle is 30 units greater than the perimeter of the square:

perimeter of the square:

perimeter of the rectangle is then

the area of the rectangle is 12 times the are of the square:

area of the square:

area of the rectangle:

let 'L' represent the length of the rectangle, then for perimeter and area of the rectangle we have,

or

substituting with :

but here

so,

the rectangle has dimensions 9x12

but   represents the length of the side of the square

so

the square has dimensions 3x3

milcah answered 2 years ago
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