A rhombus has an area of 144 square feet. One diagonal is twice the length of the other diagonal . Find the length of both diagonals.
2007-03-08 11:59:20 · 3 answers · asked by Juan C 6 in Science & Mathematics ➔ Mathematics
Note that the area of a rhombus is the product of the diagonals over 2. So a rhombus with diagonals of length a and b has area (ab)/2.
Say that the diagonals are a and b, so
a=2b.
Thus (ab)/2=144
2(b)(b)/2 = 144
b^2=144
b=12.
The length of the smaller diagonal is 12, the length of the larger is 24.
2007-03-08 12:03:00 · answer #1 · answered by Aegor R 4 · 0⤊ 0⤋
A = D*d /2 D = 2d so d^2 =144 and d=12 feet D = 24 feet
2007-03-08 20:06:18 · answer #2 · answered by santmann2002 7 · 0⤊ 0⤋
A = 1/2 diag 1(diag 2)
A = 1/2 (x)(2x)
144 = x^2
x = 12
12, and 24
2007-03-08 20:01:46 · answer #3 · answered by richardwptljc 6 · 0⤊ 0⤋