A parallelogram ABCD has perimeter equal to 124. Let E be the foot of the perpendicular from A to BC, and let F be the foot of the perpendicular from A to CD. If AE=7 and AF=24, what is the area of the parallelogram?
since area = base * height,
oops. hit wrong key.
24*AB = 7*BC
but AB+BC = 124/2 = 62, so
24(62-BC) = 7BC
BC = 48
AB = 14
Area = 24*14 = 7*48 = 336
thank you
To find the area of a parallelogram, we need to know the length of the base and the height.
From the given information, we know that AE = 7 and AF = 24.
First, we need to find the length of BC. We can use the Pythagorean theorem in triangle ABE. The square of the hypotenuse (AB) is equal to the sum of the squares of the other two sides.
AB^2 = AE^2 + BE^2
AB^2 = 7^2 + BC^2
Similarly, we can find the length of CD. We can use the Pythagorean theorem in triangle ADF.
AB^2 = AF^2 + BF^2
AB^2 = 24^2 + CD^2
Now, since ABCD is a parallelogram, opposite sides are equal in length. Therefore, we can set BC = CD = x.
Substituting the values from the two equations, we get:
7^2 + x^2 = 24^2 + x^2
49 = 576
This equation is not possible, which means there is an error in the given information.
Please verify the values of AE and AF, or provide any additional information so we can find the correct answer.