One of the diagonals of the rhombus is 4 cm larger than the other. the side of the rhombus is 10 cm.

One of the diagonals of the rhombus is 4 cm larger than the other. the side of the rhombus is 10 cm. find the length of each diagonal.

Let us denote by the variable a the length of the first diagonal, and by the variable b the length of the second diagonal.

Accordingly, according to the conditions, the first equation will be:

a = b + 4.

Therefore, according to the conditions, the second equation will be:

(a / 2) ^ 2 + (b / 2) ^ 2 = 10 ^ 2;

a ^ 2/4 + b ^ 2/4 = 100.

Substitute a from the first into the second and calculate the lengths of the diagonals:

(b + 4) ^ 2 + b ^ 2 = 400;

2b ^ 2 + 8b – 384 = 0;

b ^ 2 + 4b – 192 = 0;

D = 16 – 4 (-192) = 784 = 282;

b1 = (-4 + 28) / 2 = 12;

b2 = (-4 – 28) / 2 = -16.

12 + 4 = 16.

Answer: 12 cm and 16 cm.