The diagonals of the quadrilateral are mutually perpendicular. Their sum is 43 cm and 1 of them is 5 cm larger

| February 16, 2021 | education

The diagonals of the quadrilateral are mutually perpendicular. Their sum is 43 cm and 1 of them is 5 cm larger than the second. Find the area of the quadrilateral I need with the complete solution.

1. The vertices of the quadrilateral A, B, C, D. AC and BD are diagonals.

2. According to the problem statement, one of the diagonals is 5 centimeters larger than the other. Let’s pretend that

AC – BD = 5 centimeters. AC = (BD + 5) centimeters.

3. АС + ВD = 43 centimeters (according to the problem statement).

4. Replace AC in this expression with (BD + 5):

BD + 5 + BD = 43.

2BD = 38.

BD = 19 centimeters.

AC = 19 + 5 = 24 centimeters.

5. Since the diagonals of a given quadrangle are perpendicular, this quadrilateral

is a rhombus.

6. Calculate the area (S) of the rhombus:

S = AC x BD / 2 = 24 x 19/2 = 228 centimeters².

Answer: the area of ​​a given quadrangle is 228 centimeters².



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