Question

perimeter of a triangle is 300 M if its sides are in the ratio 3:5:7 find the area of the triangle. Is the ans 1500 root 6

Answer 1

Let the sides of the triangle be 3x , 5x and 7x
so, 3x +5x+7x = 300
15x = 300
X = 20

3x = 60m
5x = 100m
7x = 140m

Semi - perimeter = 150m

Area =✓150 * ✓(150-140) * ✓(150-100) * ✓(150-60)
=✓150*✓90*✓50*✓10
=✓5*✓3*✓10*✓9*✓10*✓5*✓10*✓10
=5*10*10*3*✓3
=1500✓3

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Answer 2

Ratio of the three sides:

Side 1 : Side 2 : Side 3 = 3 : 5 : 7

Solve x:

Let x be the constant ratio:

3x + 5x + 7x = 300 m

15x = 300

x - 20 m

Find the length of the sides:

Side 1 = 3x = 3(20) = 60 m

Side 2 = 5x = 5(20) = 100 m

Side 3 = 7x = 7(20) = 140 m

Find the area:

$\text {area} = \sqrt{p(p-a)(p-b)(p-c)}$

$\text {p = } \dfrac{300}{2} = 150$

$\text {area} = \sqrt{150(150-60)(150-100)(150-140)}$

$\text {area} = \sqrt{6750000}$

$\text {area} = 1500\sqrt{3}$

Answer: The area is 1500√3