A triangle has a perimeter of 48 cm and the lengths of two of its sides are in the ratio
MATHEMATICS · Multi-part · CBSE · Mathematics · Heron's Formula · Heron's Formula
Problem
A triangle has a perimeter of 48 cm and the lengths of two of its sides are in the ratio 3:5. The area of the triangle is known to be 96cm2.
(i) Let the two sides be 3kcm and 5kcm. Express the third side in terms of k.
(ii) Form an equation in k using the given area of the triangle and solve it.
(iii) Hence determine the exact lengths of all three sides.
(iv) Verify that the lengths obtained satisfy the triangle inequality.