The length of a rectangle is 5 centimeters less then twice it's width. The perimeter of the rectangle is 26 cm. What are the dim

Question

Oksana_A [137]

3 years ago

10

The length of a rectangle is 5 centimeters less then twice it's width. The perimeter of the rectangle is 26 cm. What are the dim

ensions of the rectangle

Mathematics

1 answer:

Sedaia [141] · Answer 1 · 2022-04-17T20:32:15+03:00

Answer:

The dimensions of the rectangle are length = 7cm and width = 6cm.

Step-by-step explanation:

In order to solve for the dimensions, you will need to set up two equations in order to solve for the missing variable. Given the information that the length is 5 cm less then twice it's width, using 'L' for length and 'w' for width we get the following equation: L = 2w - 5. Perimeter is the sum of all the sides, or in the case of a rectangle P = 2w + 2L. We can then use our expression for 'L' in our perimeter formula: 26 = 2w + 2(2w - 5). First, using the distributive property we get: 26 = 2w + 4w - 10. Next, we combine like terms: 26 = 6w - 10. Then, we use inverse operations to isolate the variable: 26 + 10 = 6w - 10 + 10 to get 36 = 6w, divide both sides by 6 to get w = 6. Lastly, plug in the value of 'w' to 'L': L = 2(6) - 5 or L = 7.