A architect wants to create a rectangular room in a house. She wants it to have a total area of 255 square feet, and it should be 10 feet longer than it is wide. What dimensions should she use for the room? Round to the nearest hundredth of a foot.

a) 10.97 feet by 20.97 feet

b) 16.73 feet by 26.73 feet

c) 15.97 feet by 25.97 feet

d) 11.73 feet by 21.73 feet

b

Step-by-step explanation:

let the width be w

length=w+10

area=w(w+10)

w²+10w=255

use quadratic formular

Area of Diagram 1 = 72 unit²

Area of Diagram 2 = 190 unit²

Area of Diagram 3 = 36 unit²

Step-by-step explanation:

In each of the diagrams shown, there are triangles and rectangles.

Note that: Area of Triangle = 1/2(Base x Height)

                Area of Rectangle = Length x Breath

Area of Diagram 1

= Area of Triangle 1 (+) Area of Rectangle (+) Area of Triangle 2.

Triangle 1: height = 6 units , base = 3 units

∴ Area = 1/2 * (6 units x 3 units) ==> 1/2 * (18 unit²) ==> 9 unit²

Rectangle: Length = 9 units , Breadth = 6 units

∴ Area = 9 units x 6 units = 54 unit²

Triangle 2: height = 6 units , base = 3 units

∴ Area = 1/2 * (6 units x 3 units) ==> 1/2 * (18 unit²) ==> 9 unit²

Recall; Area of Triangle 1 (+) Area of Rectangle (+) Area of Triangle 2 = Area of Diagram.

∴ Area of Diagram 1 = 9 unit² + 54 unit² + 9 unit² = 72 unit²

Area of Diagram 2

= Area of Triangle 1 (+) Area of Rectangle (+) Area of Triangle 2.

Triangle 1: height = 10 units , base = 3 units

∴ Area = 1/2 * (10 units x 3 units) ==> 1/2 * (30 unit²) ==> 15 unit²

Rectangle: Length = 15 units , Breadth = 10 units

∴ Area = 15 units x 10 units = 150 unit²

Triangle 2: height = 10 units , base = 5 units

∴ Area = 1/2 * (10 units x 5 units) ==> 1/2 * (50 unit²) ==> 25 unit²

Recall; Area of Triangle 1 (+) Area of Rectangle (+) Area of Triangle 2 = Area of Diagram.

∴ Area of Diagram 2 = 15 unit² + 150 unit² + 25 unit² = 190 unit²

Area of Diagram 3

= Area of Triangle 1 (+) Area of Triangle 2 (+) Area of Rectangle.

Triangle 1: height = 4 units , base = 4 units

∴ Area = 1/2 * (4 units x 4 units) ==> 1/2 * (16 unit²) ==> 8 unit²

Triangle 2: height = 4 units , base = 2 units

∴ Area = 1/2 * (4 units x 2 units) ==> 1/2 * (8 unit²) ==> 4 unit²

Rectangle: Length = (8 - 2) units = 6 units, Breadth = 4 units

∴ Area = 6 units x 4 units = 24 unit²

Recall; Area of Triangle 1 (+) Area of Triangle 2 (+) Area of Rectangle = Area of Diagram.

∴ Area of Diagram 3 = 8 unit² + 4 unit² + 24 unit² = 36 unit²