Find the corners of a rhombus whose perimeter is 40 and the area is 50.

univerkov | August 11, 2021 | education

1. Vertices of the rhombus A, B, C, D. S – area of the rhombus. P is the perimeter of the rhombus. BH – height (drawn to the AD side).

2. S = AD x BH. Each side of the rhombus = P: 4 = 40: 4 = 10 units.

AB = BC = CD = AD = AD = 10 units.

BH = S: AD = 50: 10 = 5 units.

3. In a right-angled triangle ABН sine ∠A = BH / AB = 5/10 = 1/2.

An angle whose sine is 1/2 is 30 °. ∠А = 30 °

4. ∠АВН = 180 ° – ∠А – ∠СВН = 180 ° – 30 ° – 90 ° = 60 °.

5.∠В = 90 ° + 60 ° = 150 °

Answer: ∠А = ∠С = 30 °, ∠В = ∠Д = 150 °

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