Question

The sides of a triangle are in the ratio 25:14:12 and its perimeter is 510 m. The greatest side of the triangle is:​

Answer 1

Given :-

• The sides of a triangle are in the ratio 25:14:12.

• Perimeter = 510m.

To Find :-

• The greatest side of the triangle.

Solution :-

Let,

• Sides = 25x, 14x, 12x.

Explanation :-

$\implies\sf{25x + 14x + 12x = 510m}$

$\implies\sf{51x = 510m}$

Divide 510 and 51 to get the value of x.

$\implies\sf{x = \dfrac{\cancel{510}}{\cancel{51} }}$

$\implies\sf{x = \: }{\textsf{\textbf{10.}}}$

So,

• 25x = 25 × 10 = 250m.

• 14x = 14 × 10 = 140m.

• 12x = 12 × 10 = 120m.

Hence,

• Length of all side = 250m, 140m, 120m.

• Greatest side = 250m.

Answer 2

Given :- The sides of a triangle are in the ratio 25:14:12 and its perimeter is 510 m.

To Find :- The greatest side of the triangle ?

Solution :-

since sides of given ∆ are in the ratio 25 : 14 : 12 , let us assume that, the three sides of given ∆ are 25x m , 14x m and 12x m respectively where 25x m is the greatest side of the ∆ .

So,

→ Perimeter of ∆ = 510 m

→ Sum of all sides of ∆ = 510 m

then,

→ 25x + 14x + 12x = 510

→ 51x = 510

→ 51x = 51 × 10

dividing both sides by 51,

→ x = 10

therefore,

→ Greatest side = 25x = 25 × 10 = 250 m (Ans.)

Hence, The greatest side of the triangle is equal to 250 m .

Extra :-

→ Greater side = 14x = 14 × 10 = 140 m

→ Smallest side = 12x = 12 × 10 = 120 m

Verification :-

→ 250 + 140 + 120 = 510

→ 510 = 510

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