Question

The rectangle shown has a perimeter of 56 cm and the given area. It’s length is 4 more than 3 times it’s width write and solve a system of equations to find the dimensions of the rectangle

Answer 1

The length is 22 cm and the width is 6 cm

Explanation:

Let:

• l = length of the length of the rectangle (cm)
• w = length of the width of the rectangle (cm)

Equations:

`\left \{ {{2(l + w) = 56} \atop {l = 3w + 4}} \right.`

Solve Using Substitution:

We know that l is 3w + 4. So input 3w + 4 for l in the top equation.

• 2( l + w ) = 56
• 2( 3w + 4 + w ) = 56
• 2( 4w + 4) = 56
• 8w + 8 = 56
• 8w = 48
• w = 6

Plugin New Info:

Now that we solved for w, we can solve for l by inputting the value of w in the second equation

• l = 3(6) + 4
• l = 18 + 4
• l = 22

`\boxed{\text {The length is 22 cm and the width is 6 cm}}`

-Chetan K