Question

Do number 10 please, also please answer both parts.

Answer 1

Given:-

• The perimeter of the rectangle is 104 inches.
• Two unknown sides are 2(x-1) in. and 4(x+3) in.

To find:-

• The value of x.
• The area of rectangle.

Answer:-

As we know that the perimeter of a rectangle can be calculated using the formula,

`\sf \implies Perimeter = 2(length + breadth)`

And here ,

• length = 4(x + 3) in. = (4x + 12 )in.
• breadth = 2(x-1) in. = (2x - 2)in.
• Perimeter= 104in.

Now substitute the respective values in the formula stated above as ,

`\sf \implies 104 in. = 2 [4x + 12 + 2x - 2]in. \\`

`\sf \implies 104 = 2 [ 6x + 10 ]\\`

`\sf \implies 104 = 12x + 20`

`\sf \implies 12x = 84`

`\sf \implies \underline{\underline{ x = 7 }}`

Let's find out the length and breadth to find out the area as ,

• l = 4x + 12 = 4*7 + 12 = 28 + 12 = 40in.
• b = 2x - 2 = 2*7 -2 = 14 - 2 = 12in.

Hence,

`\sf \implies Area = lb \\`

`\sf \implies Area = 40 * 12 \ in.^2`

`\sf \implies \underline{\underline{ Area = 480\ in.^2}}`

And we are done!