Question

The perimeter of a triangular is 540 m and its sides are 25: 17:12. find the measurement each of its sides .​

Answer 1

Given Information:

• Perimeter = 540 m

• Sides are in the ratio = 25 : 17 : 12

To calculate:

• The measurement each of its sides.

★ Procedure:

Here, we'll assume the sides as 25x , 17x and 12x as we don't the exact measurement of sides, where x will be a constant natural number.

Then, by forming a linear equation (formula of the perimeter of triangle) we'll find the value of x and then we'll multiply with 25, 17 & 12 in order to calculate the measure of its sides.

Calculation:

Let the sides of the triangle be 25x , 17x and 12x. As we know that,

$\star \boxed {\sf{ {Perimeter}_{(\triangle)} = Sum \: of \: all \: sides }} \\ \\ \\ \bigstar \underline{\boldsymbol{According \: to \: the \: question:}} \\ \\ \\ \sf{\longrightarrow \: 540 \: m = (25x + 17x + 12x) m} \\ \\ \\ \sf{\longrightarrow \: 540 \: m = 54x \: m} \\ \\ \\ \sf{\longrightarrow \: \dfrac{540}{54} \: m = x \: m} \\ \\ \\ \longrightarrow \underline{\boxed{\sf{10 \: m = x \: m}}} \: \red{\bigstar}$

Henceforth, Sides are :

$\sf {\longrightarrow First \: Side \to 25x = 25(10) = 250 \:m \green{\bigstar} } \\ \\ \sf{ \longrightarrow Second \: Side \to 17x = 17(10) = 170 \:m \green{\bigstar} } \\ \\ \sf{ \longrightarrow Third \: Side \to 12x = 12(10) = 120 \:m \green{\bigstar} }$

Verification:

$\star \boxed {\sf{ {Perimeter}_{(\triangle)} = Sum \: of \: all \: sides }}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \rm{LHS}} \\ \\ \sf{ \longrightarrow \: Perimeter = 540 \: m} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \rm{RHS}} \\ \\ \sf{ \longrightarrow \: Sum \: of \: all \: sides = (250 + 170 + 120) \: m} \\ \\ \sf{ \longrightarrow \: Sum \: of \: all \: sides =540 \: m}$

LHS = RHS

Hence, verified!

More about triangles:

Important properties of triangle :

★ Angle sum property of a triangle :

• Sum of interior angles of a triangle = 180°

★ Exterior angle property of a triangle :

• Sum of two interior opposite angles = Exterior angle

★ Perimeter of triangle :

• Sum of all sides

★ Area of triangle :

• $\sf { \dfrac{1}{2} \times Base \times Height }$

★ Area of an equilateral triangle:

• $\sf { \dfrac{\sqrt{3}}{4} \times {Side}^{2} }$

★ Area of a triangle when its sides are given :

• $\sf { \sqrt{s[ (s-a)(s-b)(s-c) ]} }$

Where,

• S= Semi-perimeter or $\sf {\dfrac{a+b+c}{2} }$

Answer 2

☯ GIVEN.

• The perimeter of a triangular field = 540m
• its sides are 25: 17:12

☯ TO FIND.

• The measurement each of its sides .

☯ FORMULA USED.

• Heron’s Formula

✬ EXPLANATION.

Let ,

• the sides are 25x , 17x , 12 x

❒ Perimeter of a ∆ = sum of three sides

➯ 25x + 17x + 12x = 540

➯ 54x = 540

➯x = 10

✰ 1st side (a) - 25x = 25×10= 250m

✰ 2nd side(b)= 17x = 17×10= 170m

✰ 3rd side (c)= 12x = 12 × 10 =120m

❒ Semi - perimeter ( S) = a+b+c/2

➣ (250 + 170+120)/2 = 540/2 = 270 m

➣ Area of the ∆= √ S(S - a)(S - b)(S - c)

THEN,

➯ √ S(S - 250)(S - 170)(S - 120)

➯ √ 270(270 - 250)(270 - 170)(270 - 120)

➯ √ 270× 20×100×150

➯ √ 81000000

❒ Therefore, Area of the ∆= 9000 m²

✰ Hope it helps u ✰