Answer:
Question 6
- Which property are you using?
The property that both diagonals for a rectangle are equal in length
- Work
Shown below
- BD = 33
Question 7
- Which property are you using?
The diagonals of a square intersect at right angles
- Work:
As shown
- x = 11
Explanation:
Question 6
AC and BD are the diagonals of the rectangle ABCD
The diagonals of a rectangle are equal
∴ BD= AC
Substituting for AC and BD in terms of their expressions in x:
4x + 5 = 3x + 12
4x-3x + 5 = 12 --> subtract 3x from both sides
x + 5 = 12
x = 12-5 = 7
Therefore BD = 4x + 5 = 4(7) + 5 =33
Question 7
In square BELF, ∠BSE is formed by the intersection of its two diagonals BL and EF
The diagonals of a square have the following properties
- they are equal
- they bisect each other
- they form 90° angles at intersection
We will use the third property that at intersection the angles formed are of 90°. One of these 4 angles is ∠BSE
m∠BSE = 90°
But m∠BSE = 7x + 13
Equating the two:
7x + 13 = 90
7x = 90-13 = 77
x = 11