Question

Q8. If the length of the diagonal of a rhombus is 20 cm then find its perimeter.
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Answer 1

Answer:

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.