GEOMETRY: How do you find the area of a rhombus when your given the perimeter and one diagonal?

: GEOMETRY: How do you find the area of a rhombus when your given the perimeter and one diagonal?
I need help with my Geometry. I know that the formula for the area of a rhombus is A = 1/2d1d2 (A = 1/2(diagonal1)(diagonal2). Here is the question.

5. Find the area of a rhombus with a perimeter of 100 meters and one diagonal with a length of 48 meters.

How do you find the other diagonal in order to plug it in to the formula?

Answers and Views:

Answer by skeptical
This might help:

https://www.elearnenglishlanguage.com/difficulties/youryoure.html

Answer by Evan
The two diagonals of a rhombus are perpendicular and bisect each other. If you draw the rhombus, you should see that you have 4 “right” triangles in the middle. Each triangles three sides are
1) 1/2 Length of 1 diagonal
2) 1/2 Length of the other diagonal
3) Length of the side of the rhombus.

The length of one side of the rhombus is 1/4 the perimeter (since all 4 sides are the same length), so 100/4 = 25

1/2 the length of the first diagonal is 48 / 2 = 24

1/2 the length of the other diagonal can be calculated by the pythagorean theorem, Call it x. Then x^2 + 24^2 = 26^2

x = 7

Thus the other diagonal has total length 14, and you should be able to finish the problem since you’ve gotten all the pieces of the formula you wrote.

Answer by Rob T
The diagonals bisect each other at right angles.

You have a right angled triangle with sides 1/2 d1, 1/2 d2, and 1/4 p where p is the perimeter
1/2 d1 = 24
1/4 p = 25
By Pythagoras’s theorem
1/2 d2 = 7
Area = (1/2).48.14 = 336