Question

The base of a rectangle is 4 inches greater than the height. The area of the rectangle is 15 square inches. What are the dimensions of the rectangle to the nearest tenth of an inch?

height:_______________ in.
base: _______________ in.

Answer 1

The height of the rectangle is 3 inches and the base is 7 inches.

Step-by-step explanation:

To find the dimensions of the rectangle, let's assign variables:

Height = h inches

Base = h + 4 inches

Now we can use the formula for the area of a rectangle: Area = Height * Base

Substitute the given area of 15 square inches and the expressions for height and base:

15 = h * (h + 4)

Expand the equation:

15 = h^2 + 4h

Rewrite the equation in standard form:

h^2 + 4h - 15 = 0

Factoring or using the quadratic formula, we find two possible values for h:

h = -5 or h = 3

Since the height cannot be negative, we can discard the negative value. Therefore, the height is 3 inches.

The base is the height plus 4 inches, so the base is 3 + 4 = 7 inches.

Answer 2

The dimensions of the rectangle to the nearest tenth of an inch include:

height: 2.4 in.

base: 6.4 in.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = Bh

Where:

• A represent the area of a rectangle.
• B represent the breadth of a rectangle.
• h represent the length or height of a rectangle.

Since the base of a rectangle is 4 inches greater than the height, we have;

B = 4 + h

By substituting the given parameters into the formula for the area of a rectangle, we have the following;

15 = (4 + h)h

`15 = 4h + h^2\\\\h^2+4h-15=0\\\\h = (-b\; \pm \;√(b^2 - 4ac))/(2a)\\\\h = (-4\; \pm \;√(4^2 - 4(1)(-15)))/(2(1))\\\\h = (-4\; \pm \;√(16 +60))/(2)\\\\h = (-4\; \pm \;√(76))/(2)\\\\h=-2\pm(√(76) )/(2)`

h = 2.359 ≈ 2.4 in.

For the base, we have:

b = 4 + h

b = 4 + 2.4

b = 6.4 in.

In conclusion, the dimensions of the rectangle are 2.4 by 6.4 inches.