these two questions are tricky?

Question

1. 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. Explain it bro.

2. Below is a square split into four rectangular parts. The areas of two of the parts are provided. The lengths of the sides are whole numbers. Find the area of the entire square. Write a clear and concise explanation to justify your answer.

http://i49.photobucket.com/albums/f283/mystalkingshadow/06_04h_06a.gif



- ya it is school work no I cannot get the first one but they still are interesting questions though

Answer 1

if area of rhombus is 7.5 and the area of a rhombus is
.5 x d1 x d2
then 7.5 = .5 x N x 2N+1
divide both sides by .5
15= N(2N+1)
guess and check?

first u need to know what the sides are..
the smaller rectangles sides are 2 and 4 and the bigger one is 5 and 7
since the entire four sided figure is a square.. then both sides have to be the same.. so you have to figure out which two pairs of the 4 provided side lengths add up to the same number.. in this case its 9 (5 and 4..7 and 2) then you multiply 9 times 9 and get the answer 81

Answer 2

1. if A is the long diagonal then the other (B) is twice (2B) and add 1 to it to make them equal. So 2B+1=A. A is the long diagonal and B the short diagonal.
Area =.5 AB=7.5 so AB=15 A=15/B
substitute into 2B+1=A=15/B 2B^2+B-15=0

(2B-5)(B+3)=0
2B-5=0 2B=5 B=2.5 so A=6
Also B= -3 but this is not possible in real life.



2. Since it is a square then each side is X.
Area = X^2

Area 1=8 which is 8x1 or 2x4
Area 2=35 which can be 5x7 or 1x35 in whole numbers.
so the question becomes what combination of factors of 8 and 35 yields equal sides Ans= 9x9 using 5x7 & 4x2
5&4 is 9 and 7&2 is 9

Answer 3

area of a rhombus =(1/2)a*b

where a and b are diagonals

now it is given b=2a+1
hence (1/2)a*(2a+1)=7.5
=>2a^2+a=15
just solve the quadratic and you will get a=2.5 or -3
as length can not be negative a=2.5
b=6


second q.

as sides of rectangles are in whole numbers tehey can be

35=(1,35) or (5,7)
and 8=(1,8) or (4,2)

5,7 and 4,2 fits just arrange them so that each side is equal
( 5+4=7+2=9)

so each side is equal to 9

hence area =81 sq. units

Answer 4

1.
A = d1*d2/2 = 7.5
d1 = 2d2 + 1
d1 = 15/d2
15/d2 = 2d2 + 1
2d2^2 + d2 - 15 = 0
(2d2 - 5)(d2 + 3) = 0
d2 = 5/2
d1 = 6

6(5/2)/2 = 15/2 = 7.5

2.
8 = 2*4
35 = 7*5
2 + 7 = 9
5 + 4 = 9
A = 81

8 + 35 + 10 + 28 = 81