687/VB03. problem / Math - Solved Math Problems

MR-687 / 8. problem

The area of the parallelogram is 36 m², and the distances between the intersecting point of the diagonals and the sides are 2 m and 3 m. Calculate the perimeter of the parallelogram.

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Source: Vene T. Bogoslavov: Collection of Solved Problems #3 - 8..)

Geometry → Two-dimensional geometric shapes → Quadrilaterals

$\frac{h_{a}}{2} = 2$

$h_{a} = 2 \cdot 2 = 4$

$\frac{h_{b}}{2} = 3$

$h_{b} = 2 \cdot 3 = 6$

$A = a \cdot h_{a} = b \cdot h_{b} = 36$

$A = a \cdot 4 = b \cdot 6 = 36$

$a = \frac{36}{4} = 9$

$b = \frac{36}{6} = 6$

$P = 2 (a + b) = 2 (9 + 6) = 2 \cdot 15$

$P = 30$

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