The perimeter of a rhombus is 20cm and one of its diagonal is 6cm long find the length of the other diagonal
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Ok...first Its perimeter is 20 so It has four same sides ...each side is 5cm.
And One of its diagonal is 6 ...So other one divides it in half so each half is three.
If we imagine it forms right triangle and (3,4,5 ) are triplets...so We got the half of other diagonal
So 4+4=8 is the length of other diagonal
And One of its diagonal is 6 ...So other one divides it in half so each half is three.
If we imagine it forms right triangle and (3,4,5 ) are triplets...so We got the half of other diagonal
So 4+4=8 is the length of other diagonal
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The perimeter of a rhombus is 20cm. One of its diagonals is 6cm long. What is the length of the other diagonals?
8 cm.
The diagonal of a rhombus divides the rhombus into two congruent isosceles triangles. Each isosceles triangle can be divided into two congruent right triangles. The right triangle will have 1/4 the perimeter as the hypotenuse, and 1/2 the diagonal as one leg. Then use the pythagorean theorem to find the other leg, which will be 1/2 the other diagonal.
20/4 = 5, the hypotenuse is 5 cm.
6/2 = 3 cm, one leg of the right triangle is 3.
Now you have a right triangle with hypotenuse, 5 cm and one leg of 3 cm.
Take the square root of (5^2 -3^2) = sqrrt (25 -9) = sqrrt (16) = 4 cm. Or you might recognize 3 and 5 as part of the famous 3–4–5 pythogorean triple, and just know the other side is 4 cm.
The other diagonal will be 4 cm doubled 8 cm.
8 cm.
The diagonal of a rhombus divides the rhombus into two congruent isosceles triangles. Each isosceles triangle can be divided into two congruent right triangles. The right triangle will have 1/4 the perimeter as the hypotenuse, and 1/2 the diagonal as one leg. Then use the pythagorean theorem to find the other leg, which will be 1/2 the other diagonal.
20/4 = 5, the hypotenuse is 5 cm.
6/2 = 3 cm, one leg of the right triangle is 3.
Now you have a right triangle with hypotenuse, 5 cm and one leg of 3 cm.
Take the square root of (5^2 -3^2) = sqrrt (25 -9) = sqrrt (16) = 4 cm. Or you might recognize 3 and 5 as part of the famous 3–4–5 pythogorean triple, and just know the other side is 4 cm.
The other diagonal will be 4 cm doubled 8 cm.
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