Question

The length of the sides of a triangle are in the ratio 3:4::5 and its perimeter is 144 cm. Find the area of the triagnle and the height corresponding to the longest side.

Answer 1

Answer:

The area of triangle is 864 cm² and the height corresponding to the longest side is 28.8 cm.

Step-by-step explanation:

The length of the sides of a triangle are in the ratio 3:4:5. Let the length of sides be 3x,4x,5x.

It is given that the perimeter of the triangle is 144 cm.

$3x+4x+5x=144$

$12x=144$

$x=12$

The value of x is 12. It means the length of sides are 36,48,60.

Using heron's formula the area of triangle is

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

Where,

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

$s=\frac{144}{2}=72$

The area of triangle is

$A=\sqrt{72(72-36)(72-48)(72-60)}=864$

The area of triangle is 864 cm².

The area of triangle is

$A=\frac{1}{2}\times base \times height$

$864=\frac{1}{2}\times 60 \times height$

$height=\frac{864}{30}=28.8$

The height corresponding to the longest side is 28.8 cm.

Answer 2

Answer:

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Step-by-step explanation:

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