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
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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