Question

11. The ratio of the measures of the sides of a triangle is 21:8:14. If the perimeter of the triangle is 215 feet, find the length of each side.

Answer 1

Answer:105cm,40cm,70cm

Step-by-step explanation:

Answer 2

$\large\sf\underline{Given\::}$

• Ratio of measures of sides of a triangle are 21 : 8 : 14 .

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$\large\sf\underline{To\:find\::}$

• Length of each side.

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$\large\sf\underline{Assumption\::}$

Let the length of sides of a triangle be :

• 21x

• 8x

• 14x

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$\large\sf\underline{Solution\::}$

We know :

$\small{\underline{\boxed{\mathrm\pink{Perimeter\:of\:a\:∆\:=\:a+b+c}}}}$

where

• a , b and c are three sides of a triangle

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Now substituting the given value in the formula :

$\sf\implies\:215\:=21x+8x+14x$

$\sf\implies\:215\:=43x$

$\sf\:oR\:43x\:=\:215$

• Transposing 43 to the other side

$\sf\implies\:x\:=\frac{215}{43}$

$\large{\mathfrak\red{\implies\:x\:=\:5\:feet}}$

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So now substituting the value lf x in the assumed value we get,

• 21x = 21 × 5 = $\small\fbox\red{105\:feet}$

• 8x = 8 × 5 = $\small\fbox\red{40\:feet}$

• 14x = 14 × 5 = $\small\fbox\red{70\:feet}$

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!! Hope it helps !!