Area of Picture and the Rectangular Frame is same.
and the area of the entire reagion is 18in * 15in = 270in
So area of the Picture is 270in / 2 = 135 in.
now the ratio is 15:18 i.e 5:6
So 5x * 6x = 135
30x^2 = 135
x^2 = 135 / 30
x^2 = 4.5
x^2 = 9/2
x = 3/root2
now lenght = 6x
= 6 * 3 / root 2
= 9 root 2
Ans A.
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Set 34 #15
Source: Beat The GMAT — Problem Solving |
IMO A
Suppose length of pic = x, width of pic = y
x/y=18/15 ------(1)
area of pic = xy
area of frame = 18*15-xy
Now, the question says 18*15-xy = xy => 2xy = 18*15 => xy = 9*15 ----(2)
Solve (1) and (2) to get x = 9root2
Suppose length of pic = x, width of pic = y
x/y=18/15 ------(1)
area of pic = xy
area of frame = 18*15-xy
Now, the question says 18*15-xy = xy => 2xy = 18*15 => xy = 9*15 ----(2)
Solve (1) and (2) to get x = 9root2
-
niks_01.27
- Senior | Next Rank: 100 Posts
- Posts: 45
- Location: Cleveland, OH
Equation1: 18/15 = a/b;  b = 15 x a/18
Equation2: Area (Outer Rectangle) = Area (Frame) + Area (Inner Rectangle)
But; Area (Frame) = Area (Inner Rectangle)
Area (Outer Rectangle) = 2 x Area (Inner Rectangle)
18 x 5 = 2 x a x b (a & b side of inner rect.)
Equating the value of b; a = 9 root(2)
Answer is A
Equation2: Area (Outer Rectangle) = Area (Frame) + Area (Inner Rectangle)
But; Area (Frame) = Area (Inner Rectangle)
Area (Outer Rectangle) = 2 x Area (Inner Rectangle)
18 x 5 = 2 x a x b (a & b side of inner rect.)
Equating the value of b; a = 9 root(2)
Answer is A
regards
niks...
niks...
