Respuesta :
Answer:
The wide of the rectangle = 42 inches
The length of the rectangle = 43 inches
Step-by-step explanation:
Step(i):-
Given that the length of the rectangle = 10x-7
Given that the width of the rectangle = 6x +12
The perimeter of the rectangle = 2(length + width)
Given that the perimeter of the rectangle = 170
Step(ii):-
2(length + width) = 170
length + width = 85
10x-7 +6x +12 =85
16x +5 = 85
16x = 85-5 = 80
x = [tex]\frac{80}{16}[/tex]
x = 5
Final answer:-
The length of the rectangle = 10(5)-7 = 50-7 = 43
The wide of the rectangle = 6x +12 = 6(5) + 12 = 30+12 =42
The perimeter is the sum of its all sides. The rectangle is 42 inches wide.
What is the perimeter of the rectangle?
The perimeter is the sum of its all sides. The perimeter of the rectangle is twice the sum of its length and its width.
[tex]\rm \text{Perimeter of rectanle}=2(Length +Breadth)[/tex]
As it is given to us that the length of the rectangle is (10x-7), while the width of the rectangle is (6x+12). Also, the perimeter of the rectangle is 170 inches. Therefore, using the formula of the perimeter of the rectangle we will get,
[tex]\rm Perimeter=2(Length +Breadth)\\\\170=2[(10x-7)+(6x+12)]\\\\170=2{10x-7+6x+12}\\\\170=2(16x+5)\\\\170=32x+10\\\\32x=160\\\\x=\dfrac{160}{32} = 5[/tex]
Now, substitute the value of x,
The width of the rectangle = 6x + 12 = 6(5)+12 = 30+12 = 42 inches.
Thus, the width of the rectangle is 42 inches.
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