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What is the area of a rectangle whose diagonal is 17 cm with a perimeter of 460 mm explaining work with answer?
Wiki User
∙ 9y ago
The area of rectangle is : 7820.0
Joanie Koelpin
Wiki User
∙ 9y ago10mm = 1 cm → 460mm = 460 ÷ 10 cm = 46 cm
Perimeter = 2 x (length + width)
→ length + width = perimeter ÷ 2 = 46 cm ÷ 2 = 23 cm
→ length = 23 cm - width
area = length x width
→ area = (23 - width) x width = 23 x width - width^2 [1]
Using Pythagoras:
length^2 + width^2 = diagonal^2
→ length^2 + width^2 = 17^2
→ (23 - width)^2 + width^2 = 17^2
→ 23^2 - 46 x width + width^2 +width^2 = 17^2
→ 2 x width^2 - 46 x width + 529 - 289 = 0
→ 2 x width^2 - 46 x width + 240 = 0
→ width^2 - 23 x width + 120 = 0
→ 120 = 23 x width - width^2 = area (from [1] above])
→ area = 120 cm^2
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