Answer: (A) The longer side in the rectangle is 45 units.
(B) The line LP measures 14 cm.
Step-by-step explanation: In the rectangle, two sides are given as 2x and 3x + 3, respectively. The perimeter is also given as 146 units. The formula to determine the perimeter is
Perimeter = 2(L + W)
We can now substitute for the values
146 = 2(2x + 3x + 3)
146 = 2(5x + 3)
146 = 10x + 6
Subtract 6 from both sides of the equation
140 = 10x
Divide both sides of the equation by 10
14 = x
With the value of x now known as 14, the sides of the rectangle are,
L = 2x
L = 2 x 14
L = 28
And the other side is
W = 3x + 3
W = 3(14) + 3
W = 42 + 3
W = 45
Therefore the longer side is 45 units.
In question B;
The rhombus has all sides congruent as one of its properties. This simply implies that the diagonal from point M to point O, is the same length as the diagonal from point L to point N. Hence, at point P, where both diagonals intersect, both diagonals are divided into two equal lengths each. If line LN is 28 cm, then line LP which is half of LN shall be 28 divided by 2, and that gives us 14 cm.
