Respuesta :
Answer:
so width of border is 10 inches
Step-by-step explanation:
Given data
board size = 12 * 16 inches
border area = 380 square inches
to find out
width of border
solution
let us assume width of border is x
first we find area of board i.e. 12 × 16 = 192 sq inches
and border area is given = 380 square inches
so total area of border and board is 192 + 380 = 572 sq inches
so we can say ( x+ 12 ) (x +16 ) = 572
solve this equation we get
x² +16x + 12x + 192 = 572
x² + 28x + 192 = 572
x² + 28x - 380 = 0
solve this equation and we get two value of x i.e.
x = 10 and x = -38
we will consider positive value here
so width of border is 10 inches
Answer:
The width of the border is 5 inches.
Step-by-step explanation:
Let x be the width of the border,
Given,
The rectangular board has the dimension 12 inches by 16 inches,
Thus, the dimension of the figure by joining the border with the board is,
(12+2x) inches by (16+2x) inches,
= (12+2x)(16+2x)
Hence, the area of the border = area of the figure by joining the border with the board - area of the board
= (12+2x)(16+2x) - 12 × 16
According to the question,
The area of the border = 380 square​ inches,
[tex](12+2x)(16+2x) - 12\times 16=380[/tex]
[tex]192+24x+32x+4x^2-192=380[/tex]
[tex]4x^2+56x-380=0[/tex]
[tex]4x^2+76x-20x-380=0[/tex]
[tex]4x(x+19)-20(x+19)=0[/tex]
[tex](4x-20)(x+19)=0[/tex]
By zero product property,
[tex]x=5\text{ or }x=-19[/tex]
Since, width can not be negative,
Hence, the width of the border is 5 inches.
