A triangle has side lengths of (4.6x-4.4y)(4.6x−4.4y) centimeters, (7.5x-8.8z)(7.5x−8.8z) centimeters, and (7.7z-9.2y)(7.7z−9.2y) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

The expression that represents the perimeter, in centimeters, of the triangle is cm OR 77.41x²+104y²+136.73z²-40.48xy-132xz-141.64yz centimeters

From the question, the side lengths are

(4.6x-4.4y)(4.6x−4.4y) cm, (7.5x-8.8z)(7.5x−8.8z) cm, and  (7.7z-9.2y)(7.7z−9.2y) cm.

First, we will clear the brackets one after the other

For  (4.6x-4.4y)(4.6x−4.4y) cm

∴ (4.6x-4.4y)(4.6x−4.4y) cm = cm

For  (7.5x-8.8z)(7.5x−8.8z) cm

∴ (7.5x-8.8z)(7.5x−8.8z) cm =  cm

For (7.7z-9.2y)(7.7z−9.2y) cm

∴ (7.7z-9.2y)(7.7z−9.2y) cm =   cm

Now, for the expression that represents the perimeter of the triangle,

Perimeter of a triangle can be calculated by determining the sum of all its sides

That is,

Perimeter of the triangle =   cm +  cm + cm

Collect like terms

cm

Hence, the expression that represents the perimeter, in centimeters, of the triangle is cm OR 77.41x²+104y²+136.73z²-40.48xy-132xz-141.64yz centimeters

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one of each metals

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