Kristina made rectangular place mats for her dining room table, as shown below. The area of each place mat is 135 square inches. The width of each place mat is 9 inches. How many inches long are all the sides of the place mat?
We can start by using the formula for the area of a rectangle:
Area = length x width
We know that the width is 9 inches and the area is 135 square inches, so we can solve for the length:
135 = length x 9
length = 135/9
length = 15
So each place mat is 15 inches long.
To find the perimeter (the total length of all the sides), we can use the formula:
Perimeter = 2 x length + 2 x width
Plugging in the values we know, we get:
Perimeter = 2 x 15 + 2 x 9
Perimeter = 30 + 18
Perimeter = 48
So all the sides of the place mat add up to 48 inches.
To find the length of the place mat, we need to divide the area of the place mat by its width.
Given that the area of each place mat is 135 square inches and the width is 9 inches, we can:
1. Set up the equation: Area = Length × Width
135 square inches = Length × 9 inches
2. Solve for the length by dividing both sides of the equation by 9:
Length = 135 square inches ÷ 9 inches
Length = 15 inches
Therefore, the length of each side of the place mat is 15 inches.
To find the length of each place mat, we can use the formula for the area of a rectangle:
Area = Length × Width
Since the area of each place mat is 135 square inches and the width is given as 9 inches, we can rearrange the formula to solve for the length:
Length = Area / Width
Plugging in the values:
Length = 135 square inches / 9 inches
Length = 15 inches
Therefore, each place mat is 15 inches long.
Since a rectangle has two equal pairs of sides, the total length of all the sides of the place mat would be:
2 × (Length + Width)
= 2 × (15 inches + 9 inches)
= 2 × 24 inches
= 48 inches
Therefore, all the sides of the place mat would be 48 inches long.