Question

perimeter of a triangle is 30cm and it's area is 30cmsquare. if largest side measure 13cm what is length of smallest side of the triangle​

Answer 1

Answer:

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Answer 2

The length of smallest side of triangle is 5 cm

Solution:

Given that,

Let the smallest side be x cm

The largest side measure 13 cm

perimeter of a triangle is 30cm

We know that,

perimeter = side + side + side

30 = x + 13 + side

30 - 13 - x = side

side = 17 - x

Thus, the other side is 17 - x

Given that area is 30 square cm

By formula,

$Area = \sqrt{s(s-a)(s-b)(s-c)}$

Where, a, b, c are sides of triangle

s is half of perimeter

s = 30/2 = 15

Here,

a = x

b = 13

c = 17 - x

Therefore,

$30 = \sqrt{15(15-x)(15-13)(15-17+x)}\\\\30 = \sqrt{15 \times 2 \times (x-2) \times (15-x)}\\\\30 = \sqrt{30 \times (x-2) \times (15-x)}\\\\Take\ square\ root\ on\ both\ sides\\\\30^2 = 30(x-2)(15-x)\\\\900 = 30(x-2)(15-x)\\\\(x-2)(15-x) = 30\\\\15x - x^2 -30+2x = 30\\\\x^2 -17x +60=0\\\\(x-12)(x-5) = 0\\\\x = 12\ or\ x = 5$

We have to find the length of smallest side of triangle

Therefore, length is 5 cm

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