Question

The length of sides of a triangle are in the ratio 3:4:5 and its perimeter is 144cm. Find its altitude on the longest side .
Please answer this question.

Answer 1

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Here is the solution:

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Ratio of the three sides =  3 : 4 : 5 (Given)

Define x:

Let x be the constant ratio

Ratio of the three sides =  3x : 4x : 5x

Form equation and solve x:

The perimeter is 144 cm

3x + 4x + 5x = 144

12x = 144

x = 12 cm

Find the sides:

3x = 3(12) = 36 cm

4x = 4(12) = 48 cm

5x = 5(12) = 60 cm

Find area:

Semi-perimeter, p = 144 ÷ 2 = 72

Area = √p(p - a)(p - b)(p - c)

Area = √72(72 - 36)(72 - 48)(72 - 60)

Area = 864 cm²

Find the altitude on the longest side:

Area = 1/2 x base x height

864 = 1/2 x 60 x height

30 x height = 864

height = 864 ÷ 30 = 28.8 cm

Answer: The height is 28.8 cm

Answer 2

$\huge\textbf{SOLUTION}$
$<b>$
Let the sides of the triangle be 3x cm, 4x cm and 5x cm

Perimeter of the triangle= (a+b+c)unit.

Given,Perimeter of the triangle = 144 cm

∴ 3x + 4x + 5x = $\mathbf{144}$

=>x = 12

So, the sides of the triangle are :

3x = 3 × 12 = 36 cm

4x = 4 × 12 = 48 cm

5x = 5 × 12 = 60 cm

$Semi perimeter = \frac{a + b + c}{2} \\ = \frac{36 + 48 + 60}{2} \\ \\ = \frac{144}{2} \\ \\ = 72 \: cm$
$AREA \: \: OF \: \: THE \: \: TRIANGLE= \sqrt{s(s - a)(s - b)(s - c)} \: \\ \\ = \sqrt{72(72 - 36)(72 - 48)(72 - 60)} \\ \\ = \sqrt{72(36)(24)(12} \\ \\ = 864c {m}^{2}$

Longest side = 60 cm

$Also, Area of triangle = \frac{1}{2} \times Base \times Height \\ \\ 864 = \frac{1}{2} \times 60 \times h(height) \\ \\ 864 = 30h \\ \\ \frac{864}{30} = h \\ \\ h = 28.8cm$

$\boxed{\bold{Thanks}}$

Have a colossal day ahead

$\boxed{\bold{Be Brainly}}$