Please help worth 25 points A rectangle has a base that is three feet longer than its height. The area of the rectangle is 54 square feet. What are the dimensions of the rectangle?

h=6 feet

Step-by-step explanation:

Given: 1. The base of a rectangle is three feet longer than its height.

2.Are of the rectangle=54 square meters

Let us say the rectangle has height h and base(breadth) b.

Since, the base of the rectangle is three feet longer than the height, we have b=h+3.

Also, Area of the Rectangle= hb

therefore, 54=h(h+3)

54= h2+ 3h

h2+3h-54=0 (Subtract 54 from both the sides)

To find the value of h we have to solve the quadratic equation.

[We have the equation in the form ax2+bx+c=0, to factorise the equation-

Step1. Find two numbers such that their multiplication is equal to ac and their addition is equal to b.

Step2. Replace b with these numbers.

Step3. Simplify the equation]

So, h2+3h-54=0

h2+9h-6h-54=0

h(h+9)-6(h+9)=0

(h+9)(h-6)=0

Which gives-

h= -9 or h= 6

As h is the height of the rectangle, h can not be -9.

so h=6 feet

and b=h+3=9 feet

So the dimensions of the rectangle are 6 feet for the height and 9 feet for the base.

step-by-step explanation: