Question #134995
The area of a rhombus is 143m2. If the longer diagonal is 26m,
find the length of one side of the rhombus and its altitude.
1
Expert's answer
2020-09-27T16:37:53-0400

The area of any convex quadrilateral can be determined as S=12d1d2sinφS = \frac{1}{2}d_1 d_2 \sin\varphi , where d1d_1 and d2d_2 are the diagonals, φ\varphi is the angle of diagonals' intersection (90 degrees for a rhombus).

Thus, the formula simplifies to S=12d1d2S = \frac{1}{2}d_1 d_2. From here, d2=2Sd1=11d_2 = \frac{2S}{d_1}=11 m.

Then, if we take one quarter of a rhombus, we will have a right triangle with diagonals' halves as shorter sides of triangle and side of the rhombus as hypotenuse.

Hence, side of the rhombus a = 132+5.52=14.1155914.12\sqrt{13^2+5.5^2}=14.11559\approx14.12 m. <---------------------------

The last thing to calculate is the altitude h. From S=ahS=a\cdot h we get h=Sa=10.1306410.13h=\frac{S}{a}=10.13064\approx10.13 m. <-----------------------------


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