Question

The ratio of the measures of three sides of
a triangle is 4:2:3 and its perimeter is
36 cm. Find the area of this triangle.​

Answer 1

Answer:

taking sides of triangle in ratio of 4x, 2x, 3x and perimeter is 36 cm.

Therefore, perimeter of triangle = Sum of all sides

36 = 4x + 2x + 3x

36 = 9x

4 = x

x = 4

Therefore , sides of triangle are

4x = 4×4 = 16 cm

2x = 2×4 = 8 cm

3x = 3×4 = 12 cm

Now, using heron's formula

s = (a+b+c)/2

s = (16+8+12)/2

s = 36/2

s = 18

Now, Area = √s(s-a)(s-b)(s-c)

Area = √18(18-16)(18-8)(18-12)

Area = √18×2×10×6

Area = √2160

Area = 46.47 cubic cm.

Area of a triangle is 46.47 cubic cm.

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Answer 2

Let each side of the triangle be 4x, 2x and 3x

Perimeter = Sum of all sides

→ 36 = 4x + 2x + 3x

→ 36 = 9x

→ x = 36 ÷ 9

→ x = 4 cm

For finding each side of the triangle,

• 4x = 4(4) = 16 cm = a
• 2x = 2(4) = 8 cm = b
• 3x = 3(4) = 12 cm = c

Since we know the 3 sides of the triangle, we apply Herons formula to find the area of triangle.

Semiperimeter = 36 ÷ 2 = 18

So, s = 18

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

$\sf{Area = \sqrt{18(18 - 16)(18 - 8)(18 - 12)} }$

$: \implies \sf{Area = \sqrt{18(2)(10)(6)} }$

$: \implies \sf{Area = \sqrt{36 \times 60} }$

$: \implies \sf{Area = 6 \sqrt{4 \times 15} }$

$: \implies \sf{Area = 12 \sqrt{15} }$

Substitute the value of √15 as 3.87

$\\ \therefore \boxed{ \bf{Area = 46.44\: {cm}^{2} }}$