Question

A rectangle is shown. All angles are right angles. The length of one side is 2 x and the length of another side is 3 x + 3. The perimeter of the rectangle is 146 units. What is the length of the longer side? 14 units 28 units 33 units 45 units Rhombus LMNO is shown with its diagonals. Rhombus L M N O is shown. Diagonals are drawn from point M to point O and from point L to point N and intersect at point P. All sides are congruent. The length of LN is 28 centimeters. What is the length of LP? 7 cm 9 cm 14 cm 21 cm

Answer 1

Answer:

Answer: (A) The longer side in the rectangle is 45 units.

(B) The line LP measures 14 cm.

Step-by-step explanation:

Answer 2

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.