From a circular piece of metal sheet with diameter 10 cm, a rectangular piece with perimeter 28 cm is to be cut. Find the dimensions of the rectangular sheet.

Answer 1

Since the perimeter is 28, we can say:

2L + 2H = 28

L + H = 14

L = 14 - H

Since the diameter, length, and height form a right triangle (corners of a rectangle are 90º) then we can use the Pythagorean Theorem to write:

L² + H² = d²

L² + H² = 10²

L² + H² = 100 the subbing in L = 14 - H we get:

(14 - H)² + H² = 100

196 - 28H + H² + H² = 100

2H² - 28H + 196 = 100

2H² - 28H + 96 = 0

H² - 14H + 48 = 0

(H - 8)(H - 6) = 0

H = 8 or H = 6

Since L = 14 - H then L = 14 - 8 = 6 or L - 6 = 8

So, either way, the rectangle is 6 cm x 8 cm