In rectangle ABCD line EF joins the midpoint of line AB and BC. Line BE equals 5, line BF equals 12, find line EF, line AC and perimeter of the rectangle.
To find the length of line EF, we can first find the length of line BC and then use that to find the length of line AC. Finally, we can find the perimeter of the rectangle.
1. Find the length of line BC:
Since we know line BE equals 5 and line BF equals 12, we can deduce that line EF is the hypotenuse of right triangle BEF. Applying the Pythagorean theorem, we have:
EF^2 = BE^2 + BF^2
EF^2 = 5^2 + 12^2
EF^2 = 25 + 144
EF^2 = 169
EF = √169
EF = 13
2. Find the length of line AC:
Line AC is simply the diagonal of the rectangle ABCD, which can be found using the Pythagorean theorem. Since ABCD is a rectangle, lines AD and BC are parallel, and lines AB and CD are parallel. So, triangle ABC is a right triangle, and we can determine the length of AC using the following equation:
AC^2 = AB^2 + BC^2
Since AB and BC are the sides of the rectangle, we need to find the length of one of them:
AB = AD = BC = CD = (length of rectangle)
Since a rectangle has equal opposite sides, we can assume that the length of AB is the length of the rectangle, and the length of BC is the width of the rectangle.
So, let's assume the length of the rectangle is L and the width is W:
AC^2 = L^2 + W^2
AC^2 = L^2 + (EF^2 - BE^2)
AC^2 = L^2 + (13^2 - 5^2)
AC^2 = L^2 + 169 - 25
AC^2 = L^2 + 144
Now, we need more information to determine the length of the rectangle. Please provide this information.
3. Find the perimeter of the rectangle:
Once we know the length of the rectangle from step 2, we can find the perimeter by using the formula:
Perimeter = 2 * (Length + Width)
We already have the information for line EF (which is the width of the rectangle), so we only need the length again to calculate the perimeter.