If ABCD is a parallelogram, BC =3m + 10, and AD = 7m – 2, find the value of ‘m’. *
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Three important properties of the diagonals of a rhombus that we need for this problem are:
1. the diagonals of a rhombus bisect each other
2. the diagonals form two perpendicular lines
3. the diagonals bisect the angles of the rhombus
First, we can let O be the point where the two diagonals intersect (as shown in the attached image). Using the properties listed above, we can conclude that ∠AOB is equal to 90° and ∠BAO = 60/2 = 30°.
Since a triangle's interior angles have a sum of 180°, then we have ∠ABO = 180 - 90 - 30 = 60°. This shows that the ΔAOB is a 30-60-90 triangle.
For a 30-60-90 triangle, the ratio of the sides facing the corresponding anges is 1:√3:2. So, since we know that AB = 10, we can compute for the rest of the sides.
Similarly, we have
Now, to find the lengths of the diagonals,
So, the lengths of the diagonals are 10 and 10√3.
Answer: 10 and 10√3 units
1. the diagonals of a rhombus bisect each other
2. the diagonals form two perpendicular lines
3. the diagonals bisect the angles of the rhombus
First, we can let O be the point where the two diagonals intersect (as shown in the attached image). Using the properties listed above, we can conclude that ∠AOB is equal to 90° and ∠BAO = 60/2 = 30°.
Since a triangle's interior angles have a sum of 180°, then we have ∠ABO = 180 - 90 - 30 = 60°. This shows that the ΔAOB is a 30-60-90 triangle.
For a 30-60-90 triangle, the ratio of the sides facing the corresponding anges is 1:√3:2. So, since we know that AB = 10, we can compute for the rest of the sides.
Similarly, we have
Now, to find the lengths of the diagonals,
So, the lengths of the diagonals are 10 and 10√3.
Answer: 10 and 10√3 units
The shapes are similar.
When two figures are similar, the ratios of the lengths of their corresponding sides are equal.
Therefore,
Simplify:
Cross multiply:
42(10+x) = 57x
420 + 42x = 57x
420 = 57x - 42x
420 = 15x
x = (420÷15)
x = 28
When two figures are similar, the ratios of the lengths of their corresponding sides are equal.
Therefore,
Simplify:
Cross multiply:
42(10+x) = 57x
420 + 42x = 57x
420 = 57x - 42x
420 = 15x
x = (420÷15)
x = 28