Question

The first floor of a house consists of a kitchen, playroom, and dining room. The areas of the kitchen, playroom, and dining room are in the ratio 4:3:2. The combined area of these three rooms is 189 square feet.

What is the area of the kitchen?

Answer 1

The area of the kitchen is 84 square feet

Explanation:

Let

x-----> the area of the kitchen in square feet

y ----> the area of the playroom in square feet

z ----> the area of the dining room in square feet

we know that

`x+y+z=189` ----> equation A

`x:y:z=4:3:2`

so

`(x)/(y) =(4)/(3)` ---->
`y=(3)/(4)x` ---> equation B

`(x)/(z) =(4)/(2)` ---->
`z=(2)/(4)x` ---> equation C

substitute equation B and equation C in equation A

`x+(3)/(4)x+(2)/(4)x=189`

solve for x

`(9)/(4)x=189`

`x=189(4)/9\\x=84\ ft^2`

therefore

The area of the kitchen is 84 square feet