A painting, square in shape, is placed in a wooden frame with width of 10% of the length of the side of the paining. The paintin
g was enlarged by 10%. By what percent is the new frame bigger than the original frame if the width of the frame remains the same?
1 answer:
Answer:
The new frame is 8.3 % bigger.
Step-by-step explanation:
A. Original painting
Let the side of the painting = x.
Then width of frame = 0.1x
Width of frame + painting = x + 2×0.1x
Width of frame + painting = x + 0.2x
Width of frame + painting = 1.2x
=====
Area of painting = x²
Area of frame + painting = (1.2x)²
Area of frame = (1.44x² -x²)
Area of frame = x²(1.44 - 1)
Area of frame = 0.44x²
===============
B. Enlarged painting
Side of painting = 1.1x
Width of frame = 0.1x
Width of frame + painting = 1.1x+ 0.2x
Width of frame + painting = 1.3x
=====
Area of painting = (1.1x)²
Area of painting = 1.21x²
Area of frame + painting = (1.3x)²
Area of frame + painting = 1.69x²
Area of frame = 1.69x² - 1.21x²
Area of frame = (1.69 - 1.21)x²
Area of frame = 0.48x²
===============
C. % increase in area of frame
Original area = 0.44x²
New area = 0.48x²
Increase = 0.04x²
% Increase = Increase/Original × 100 %
% Increase = 0.04x²/0.44x² × 100 %
% Increase = 0.083 × 100 %
% Increase = 9.1 %
You might be interested in