Question

What is the perimeter of a triangle whose area is 40076 cm and sides are in the ratio 4:5:7?
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Answer 1

Answer:

let the sides be 4x, 5x and 7x as the given ratio is 4:5:7.

area is 40076 cm²

area of a triangle=

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

where,

$s = \frac{a + b + c}{2}$

and a, b and c are the sides of the triangle

hence a=4x,b=5x and c=7x.

$s = \frac{4x + 5x + 7x}{2}\\s = \frac{16x}{2}$

area=

$\sqrt{s (s - a)(s - b)(s - c) } \\ \sqrt{ 8x (8x - 4x)(8x - 5x)(8x - 7x) } \\ \sqrt{ 8x \times 4x \times 3x \times x } \\ \sqrt{96 {x}^{4} } \\ 4 {x}^{2} \sqrt{6}$

therefore

$40076 = 4 {x}^{2} \sqrt{6}$

x=200.19/2×2.45

x=200.19/4.9

x=40.86 cm

perimeter =4x+5x+7x

=4(40.86)+5(40.86)+7(40.86)

=163.42+204.28+285.99

=653.69cm