Question

19. The perimeter of a triangle is 16cm. If one side is 6cm, find the other two sides so
that the area of the triangle is maximum
​

Answer 1

Answer:

5 and 5

they are both 5

Step-by-step explanation:

Answer 2

Step-by-step explanation:

HEY mate ....

$given : \\ \\ p = 16 |cm| \\ \\ let \: b = x \: \\ c = 10 - x \\ \\ a + b + c = 16 |cm| \\ \\6 + b + c = 16 |cm| \\ \\ b + c = 10 |cm| \\ \\ \\ s = \frac{a + b + c}{2} = 8 \\ \\ a = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ {a}^{2} = \sqrt{8(8 - 6)(8 - x)(8 - (10 - x)} \\ \\ {a}^{2} = \sqrt{16(8 - x)(x - 2)} \\ \\ \implies \: 16(8x - {x}^{2} - 16 + 2x) \\ \\ \implies \: {a}^{2} = 16(10x - {x}^{2} - 16) \\ \\ \frac{d {a}^{2} }{dx} = 16(10 - 2x) \\ \\ \frac{d {a}^{2} }{dx} = 0 \\ \\ x = 5 \\ \\ so \: b = 5 |cm| \\ \\ c = 10 - 5 = 5cm$

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