Question

the lengths of the sides of a triangle are integers, and it's area is also integer. one side is 21 and the perimeter is 48. find the shortest side?

Answer 1

HEY DEAR .

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Sum of other 2 sides = 27.
=> If one side = x, other = 27 - x.
Using Heron's formula,
=> A^2 = 24*3*(24-x)*(x-3)
RHS must be a perfect square
=> A^2 = 6^2 * 2 * (24-x)(x-3) is a perfect square
=> x = 10, Other side = 17
=> shortest side = 10 cm.
Other sides are 17 and 21 cm,
Area = 84 sq cm.

HOPE , IT HELPS .
FOLLOW ME .

Answer 2

yaaa it is correct

Step-by-step explanation:

the answer is 10