The width and length of a rectangle are respectively 2 less and 3 more than the length of the side of a square. If the area of the rectangle is 4 more than the area of the square, find the dimension of the rectangle and the area of the square.
2007-02-25 21:44:34 · 7 answers · asked by tonia c 1 in Science & Mathematics ➔ Mathematics
Let the side of the square be x
Width of rectangle = x - 2
Length of rectangle = x + 3
Area of rectangle = 4 + Area of square
(x - 2)(x + 3) = x^2 + 4
x^2 + x - 6 = x^2 + 4
Cancel out the two x^2s
x - 6 = 4
x = 10
Area of square = 10*10 = 100 sq. units
Dimensions of rectangle = (10 - 2) * (10 + 3)
= 13 * 8
2007-02-25 23:38:27 · answer #1 · answered by Akilesh - Internet Undertaker 7 · 0⤊ 0⤋
If a is the width, which is 2 shorter than the Square (s) then
a = s -2
If b is the lengt, which is 3 longer than the squre then
b = s + 3
The area of the rectangle is 4 units larger than the area of the square then
a x b = s^2 + 4
Substitute the expressions for a and b above and
(s-2)(s+3) = S^2 + 4
s^2 - 2s + 3s - 6 = s^2 + 4
Subtract S^2 from both sides
-2s +3s - 6 = 4
s - 6 = 4
s = 10
So the width is a = s - 2 = 8 and
the length is b = s + 3 = 13
2007-02-26 06:08:10 · answer #2 · answered by Possum 4 · 0⤊ 0⤋
Let each side of the square be x units
The width of the rectangle=x-2
The length of the rectangle=x+3
By the conditions.
(x-2)(x+3)=x^2+4
x^2+x-6=x^2+4
=>x=10
Therefore the area of the sq is 100 sq units and the area of the rectangle is 104sq units
2007-02-26 06:08:16 · answer #3 · answered by alpha 7 · 0⤊ 0⤋
We have (L - 2)(L +3) = L^2 + 4
where L is the side of the square.
Solving this equation gives L = 10
Thus the dimensions of the rectangle are w = 8 and l = 13
2007-02-26 05:51:40 · answer #4 · answered by physicist 4 · 0⤊ 0⤋
We can use here the simple equation x+y+ xy/100.
The sign of operator either + or - according to less or more.
The change in the width and lenght are -2 and +3
Let's assume that the default area is 100 sqm, then the percentage change in the area would be:
-2+3+(-2*3/100) which give the positive value .94 it mean the area is increase by .94%, therefore the new dimension would be
.94*100=4X
x=(.94*100)/4=23.5
Therefore the dimension would be 23.5/2 which is11.75.
I guess it would be correct.
2007-02-26 07:27:17 · answer #5 · answered by Anonymous · 0⤊ 0⤋
(x-2)(x+3) = x*x+4
or x-6 = 4
or x =10
The dimensions of the rectangle are 13m by 8 m. The square's area is 100m^2.
2007-02-26 05:57:48 · answer #6 · answered by ag_iitkgp 7 · 0⤊ 0⤋
rectangle = 8 wide x 13 long
A of square = 100
2007-02-26 05:57:37 · answer #7 · answered by OD 4 · 0⤊ 0⤋