Question

A rectangle's area is 6 units larger than its perimeter. The height of the rectangle is 4 units. What is the base of the rectangle in units?

Answer 1

The area of a rectangle is the product of its dimensions

The base of the rectangle is 7 units

How to calculate the base of the rectangle

The area of a rectangle is:

Area (A) = Base (B) * Height (H)

From the question, we have:

A = 6 + P

H = 4

The perimeter of the rectangle is:

P =2 * (B + H)

So, we have:

P =2 * (B + 4)

Substitute P =2 * (B + 4) in A = 6 + P

A = 6 + 2 * (B + 4)

Expand

A = 6 + 2B + 8

Evaluate

A = 2B + 14

The area of the rectangle is:

A = BH

So, we have

A = 4B

Substitute 4B for A in A = 2B + 14

4B = 2B + 14

Subtract 2B from both sides

2B = 14

Divide both sides by 2

B = 7

Hence, the base of the rectangle is 7 units

Read more about areas at:

https://brainly.com/question/24487155

Answer 2

let base be x

Area=LB=4x

Now

• Area=2(L+B)+6
• 4x=2(4+x)+6
• 4x=14+2X
• 2x=14
• x=7