SOLUTION: Ms. Theodorou wants to hang a portrait of Mr Fucheck in the hallway.
The length of the picture is (x+2) and the width of the picture is (x+1).
Ms Cavazzi will build a frame out
Algebra.Com
Question 441579: Ms. Theodorou wants to hang a portrait of Mr Fucheck in the hallway.
The length of the picture is (x+2) and the width of the picture is (x+1).
Ms Cavazzi will build a frame out of wood. The Frame will have a 2 inch border.
The area of that entire Portrait will cover is 272 inches square. Find the dimensions of the picture.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Ms. Theodorou wants to hang a portrait of Mr Fucheck in the hallway.
The length of the picture is (x+2) and the width of the picture is (x+1).
Ms Cavazzi will build a frame out of wood. The Frame will have a 2 inch border.
The area of that entire Portrait will cover is 272 inches square.
Find the dimensions of the picture.
:
A 2" border will add 4" to each picture dimension
therefore
(x+2) + 4 = (x+6); overall length
(x+1) + 4 = (x+5); overall width
:
Entire area
(x+6)*(x+5) = 272
FOIL
x^2 + 6x + 5x + 30 = 272
x^2 + 11x + 30 - 272 = 0
x^2 + 11x - 242 = 0
You can solve this using the quadratic formula: a=1; b=11; c=-242
But it will factor to
(x+22)(x-11) = 0
the positive solution
x = 11
therefore
11 + 2 = 13" is the length of the picture
11 + 1 = 12" is the width
:
:
Check this by finding the overall area with these values
(13+4)*(12+4) = 272
RELATED QUESTIONS
the area of a large hallway is 24 square feet meters. the width of the hallway is 2... (answered by Alan3354,TimothyLamb)
Lucy wants her portrait to be framed of uniform width. If the dimensions of the portrait... (answered by ikleyn)
A hallway has a area of 63 square feet. The length of the hallway is 7 times longer than... (answered by Cromlix)
A rectangular hallway has an area of 70ft2. The width of the hallway is 4 feet. What is... (answered by MathLover1)
The length of a rectangular portrait is 2.5 times the width. the perimeter is 28 feet.... (answered by Cromlix)
A square room and a hallway are to have carpet laid on the floor.
123 m^2 of carpet is... (answered by josgarithmetic)
A rectangular portrait is 3 inches longer than it is wide. A 3 inch frame of uniform... (answered by sachi)
Bill has an 8 inch × 10 inch picture of his family. He wants to hang it in a frame that... (answered by josgarithmetic,ikleyn)
A frame around a family portrait has a perimeter of 90 inches. The length is fifteen less (answered by Boreal)