The area of a rhombus is 7.5 sq. in. Find the length of the two diagonals if one of them is one more than twice the other. Show all work to receive credit.
2007-10-10 15:43:17 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Area = (1/2)*Diagonal1*Diagonal2
7.5=(1/2)*(2*Diagonal2+1)*Diagonal2
0=2*(Diagonal2)^2+Diagonal2-15
quadartic formula
Diagonal2 = 2.5 and -3 (reject)
Diagonal1 = (2*Diagonal2+1) = 6
answer: 6, 2.5
2007-10-10 15:53:52 · answer #1 · answered by fcas80 7 · 0⤊ 0⤋
Let the length of the diagonals be a and b. Each half of the rhombus is a triangle whose area is (1/2)a(1/2)b = (1/4)ab, so adding the halves, area is (1/2)ab.
So 7.5 = (1/2)(x)(2x+1)
x(2x+1) = 15
2x² + x - 15 = 0
(2x - 5)(x + 3) = 0
2x - 5 = 0
x = 2.5
x+3 = 0, x = -3 is a solution we can't use.
so one diagonal is 2.5 in, other is 2(2.5)+1 = 6 in.
2007-10-10 22:56:55 · answer #2 · answered by Philo 7 · 1⤊ 0⤋