A frame measures 30 cm by 20 cm. Can you mount a square picture with an area of 500cm^2 in the frame? Explain.
So you're frame is 20cm x 30cm which gives you an area of 600cm^2. You're trying to put a picture with an area of 500cm^2 which dimensions are 22.36cm x 22.36cm. The picture will not fit because it is too big.
A square picture with an area of 100 cm^2 is mounted on a square piece of matting. The matting has 2.5 times the area of the picture. Is the picture is centered on the matting, what width of the matting is visible around the outside of the picture? Give your answer to the nearest tenth of a centimeter.
First find the area of the matting:
100cm^2 x 2.5 = 250cm^2
Fing the side length of the picture:
sqrt 100cm^2 = 10cm
Find the side length of the matting:
sqrt 250cm^2 = 15.81cm
Subtract side lengths to find visible matting:
15.81cm - 10cm = 5.81cm
Make equal on both sides of the picture to find width of visible matting:
5.81 ÷ 2 = 2.9cm
The width of the matting visible around the outside of the picture is 2.9cm.