A square has sides of length x centimeters. A new rectangle is created by increasing one dimension by 4 centimeters and increasing the other dimension by 5 centimeters.
Write two expressions, one in factored form and one in expanded form, for the area of the new rectangle.
2007-04-22 15:39:44 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The new rectangle has an area equal to its length times its breadth, which is (x+4)(x+5). The expanded form is
x^2 + 9x + 20.
2007-04-22 15:43:37 · answer #1 · answered by Isaac Laquedem 4 · 0⤊ 0⤋
All four-sided polygons have an area of length x width.
The square by itself has an area of (x)(x) = x^2
The rectangle will then have an area of (x + 4)(x+5).
This is your factored form of the answer. Now just use FOIL to multiply the factored form into the expanded form:
(x + 4)(x + 5) = x^2 + 4x + 5x + (4)(5)
simplify = x^2 + 9x + 20
That is your second answer.
Hope this helps!
2007-04-22 22:44:52 · answer #2 · answered by Ingeniero de Cervezas: Aarón 2 · 0⤊ 0⤋
One side will be (x+4) cm, the other will be (x+5). So the area will be (x+4)(x+5) in factored form, which you can expand to x^2 + 9x + 20.
2007-04-22 22:42:44 · answer #3 · answered by Scarlet Manuka 7 · 0⤊ 0⤋
Area of new rectangle
= (x+4)(x+5) ----- factorised form
= x^2 +5x + 4x + 20
= x^2 + 9x + 20 ---- expanded form
2007-04-22 22:47:03 · answer #4 · answered by QiQi 3 · 0⤊ 0⤋
(x+4)(x+5) = x^2 + 9x + 20.
2007-04-22 22:44:16 · answer #5 · answered by Anonymous · 0⤊ 0⤋