The diagonals of the rhombus are 3: 4, the side of the rhombus is 10 cm. Find the diagonals of the rhombus
July 29, 2021 | education|
The sides of the rhombus are equal by the property of the rhombus. The diagonals in it are related as 3: 4.
The diagonals of the rhombus are mutually perpendicular and are divided in half at the point of intersection, forming 4 equal right-angled triangles. The side of the rhombus is the hypotenuse, the halves of the diagonals are the legs (their ratio is 3: 4).
The legs are 3x cm and 4x cm, according to the Pythagorean theorem:
(3x) ^ 2 + (4x) ^ 2 = (10) ^ 2;
9x ^ 2 + 16x ^ 2 = 100;
25x ^ 2 = 100;
x ^ 2 = 4;
x = 2 (x = -2 does not work);
Let’s find the diagonals:
3 * 2 = 6 (centimeters) – one diagonal.
4 * 2 = 8 (centimeters) – another diagonal.
Answer: 6 cm; 8 cm.
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