Hi there! :)
<u>Answer:</u>
Length = 4 cm
Width = 9 cm
Step-by-step explanation:
Here's the information we know:
- Perimeter = 26 cm
- Width = x (I just replaced the width by "x" because it's what we are looking for)
- Length = x - 5
Now before we can do anything, you need to know what the formula for the perimeter of a rectangular is:<u> P = (2 × Length) + (2 × Width)</u>
Replace all the information you know in the formula and solve the equation by isolating "x":
P = (2 × Length) + (2 × Width)
26 = ( 2 × (x - 5)) + (<u>2 × x</u>)
Multiply "2" and "x" together → 2 × x = <u>2x</u>
26 = ( <u>2</u>(x - 5)) + 2x
Distribute the "2" to the entire parentheses → 2 × x = <u>2x</u> & 2 × -5 = <u>-10</u>
26 = <u>2x</u> - 10 + <u>2x</u>
Add similar terms together → 2x + 2x = <u>4x</u>
26 = 4x <u>- 10</u>
Add 10 to each side of the equation → 26 + 10 = <u>36</u>
36 = <u>4</u>x
Divide each side of the equation by 4 → 36 ÷ 4 = <u>9</u>
<u>9 = x ⇒ Measure of the width</u>
Since the lenght is 5 centimeter less than the measure of the width, in order to find the measure of the length you'll need to subtract "5" from the measure of the width, which is "9":
9 - 5 = Length rectangle
9 - 5 = <u>4 ⇒ Length rectangle</u>
There you go! I really hope this helped, if there's anything just let me know! :)
