QuestionFind the perimeter of rectangle where cm, cm, and area is cm².
Studdy Solution
STEP 1
Assumptions1. The figure ABC is a rectangle. The length AB is given by (x+1) cm3. The width DC is given by (x+3) cm4. The area of the rectangle is24 cm²5. The perimeter of a rectangle is given by*(length + width)
STEP 2
First, we need to find the values of x that satisfy the area of the rectangle. The area of a rectangle is given by length * width.
STEP 3
Now, plug in the given values for the length and width to calculate the area.
STEP 4
Set the calculated area equal to the given area and solve for x.
STEP 5
Expand the left side of the equation.
STEP 6
Rearrange the equation to form a quadratic equation.
STEP 7
implify the equation.
STEP 8
Factor the quadratic equation.
STEP 9
Set each factor equal to zero and solve for x.
STEP 10
olve for x.
STEP 11
Since x represents a length, it cannot be negative. Therefore, x =3.
STEP 12
Now that we have the value of x, we can find the length and width of the rectangle. Substitute x = into the expressions for the length and width.
STEP 13
Now that we have the length and width of the rectangle, we can find the perimeter. The perimeter of a rectangle is given by2*(length + width).
STEP 14
Substitute the values for the length and width into the formula for the perimeter.
STEP 15
Calculate the perimeter of the rectangle.
The perimeter of the rectangle ABC is20 cm.
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