Question

The perimeter of the bigger rectangle is 430 ft and smaller rectangle is x - 3y = 30. As per the given information, the area of bigger rectangle is .

• A. 3,562 ${\text{ft}}^2$
• B. 3,016 ${\text{ft}}^2$
• C. 8,016 ${\text{ft}}^2$
• D. 8,816 ${\text{ft}}^2$

Answer 1

The correct option is C 8,016 ${\text{ft}}^2$

Given, perimeter of a bigger rectangle is 430 ft.
$\because$ Perimeter of a rectangle = 2(l + b)
$⟹$2((3x + 5) + 6y) = 430
$⟹$6x + 10 + 12y = 430
$⟹$6x + 12y = 430 - 10
$⟹$6x + 12y = 420 ----------(1)
Perimeter of smaller rectangle is
given as
x - 3y = 30-------------(2)

Multiply equation (2) with 4 we get:
$⟹$4x - 12y = 120-------------(3)

Adding equations (2) and (3)
$⟹$6x + 12y + 4x - 12y = 420 + 120
$⟹$10x = 420 + 120
$⟹$10x = 540
$⟹$x = $\frac{540}{10}$
$⟹$x = 54

Substitute x value in equation (1)
$⟹$6(54) + 12y = 420
$⟹$324 + 12y = 420
$⟹$12y = 420 - 324
$⟹$12y = 96
$⟹$y = 8

$\because$ Area = Length $\times$ Width
= (3x + 5) $\times$ 6y
= [3(54) + 5] $\times$ 6(8)
= (162 + 5) $\times$ 48
= 167 $\times$ 48
= 8,016 ${\text{ft}}^2$