A problem by Dan Conway
The diagram shows a rectangle.
The length of the rectangle is
x
cm.
The length of a diagonal of the rectangle is 8 cm. The perimeter of the rectangle is 20 cm.
Find x . Give your solutions correct to 3 significant figures and submit the smaller value of x .
The answer is 2.35.
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1 solution
Let other side be y cm
x² + y²= 8² = 64
2(x+y) = 20 so x + y = 10
(x + y)² = x² + y² + 2xy
100 = 64 + 2xy
xy = 18
x(10 – x) = 18
x² – 10x + 18 = 0
x = 5 ± √7 smaller value = 5 – √7 = 2.35