Answer:
a. Larger: 16x +5; Smaller: 4x +5
b. Difference: 12x
c. Larger: 53; Smaller: 17
Explanation:
You want expressions for the perimeter of each triangle, the difference of those, and their value when x=3.
a. Perimeter
The perimeter is the sum of the side lengths. The expression is simplified by combining like terms.
Larger: (4x +2) +(7x +7) +(5x -4) = (4+7+5)x +(2+7-4) = 16x +5
Smaller: (x +3) +(2x -5) +(x +7) = (1+2+1)x +(3-5+7) = 4x +5
The perimeter of the larger triangle is 16x +5; the smaller, 4x +5.
b. Difference
The difference is found by subtracting the smaller from the larger. Like terms can be combined.
(16x +5) -(4x +5) = (16 -4)x +(5 -5) = 12x
The difference in perimeters is 12x.
c. Value
When x = 3, the larger triangle perimeter is ...
16·3 +5 = 48 +5 = 53 . . . . units
and the smaller triangle perimeter is ...
4·3 +5 = 12 +5 = 17 . . . . units
The perimeters of the larger and smaller triangles are 53 units and 17 units, respectively, when x = 3.
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Additional comment
There are no values of x that will make the larger triangle be a right triangle. The smaller triangle is a right triangle only for x = 10+√116.5 ≈ 20.794.
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