Given the area and perimeter of the rectangular dining room, the dimensions of the dining room are 8m by 8m.
The area of rectangle is expressed as;
A = l × b
The perimeter of a rectangle is expressed as;
P = 2( l + b )
Given that;
We use the information given to form a system of equations.
A = l × b
64 = l × b
P = 2( l + b )
32 = 2( l + b )
Hence, we have;
64 = l × b --------- equ 1
32 = 2( l + b )-----equ 2
Lets make l the subject of the formula in equation 1
64 = l × b
l = 64/b -------------equ 3
Substitute equation 3 into equation 2
32 = 2( l + b )
32 = 2l + 2b
32 = 2(64/b) + 2b
32 = 128/b + 2b
Now, we solve for b.
32 = 128/b + 2b
32 - 2b = 128/b
32b - 2b² = 128
2b² - 32b + 128 = 0
We factor out 2
2( b² - 16b + 64) = 0
From perfect square rule
2( 8-b )² = 0
divide both side by 2 and take the square root of both side
( 8-b )² = 0
8-b = 0
b = 8
Substitute b=8 into equation 1
64 = l × b
64 = l × 8
l = 64/8
l = 8
Given the area and perimeter of the rectangular dining room, the dimensions of the dining room are 8m by 8m.
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