Question

the area of the floor of a rectangular room is 84 square feet. The length of the room is 5 feet more than its width. Find the width and the length of the room
a. 7 feet and 12 feet
b. 8 feet and 11 feet
c. 7 feet and 11 feet
d. 8 feet and 12 feet​
explain!!!​

Answer 1

Answer:

a. 7 feet and 12 feet

.

Short Trick :

See options, only one option has difference between sides as 5 feet as given in the question.

Step-by-step explanation:

Let Width be x, Length = (x+5) feet

Area = Length * Width = x (x+5) = x^2 + 5x

=> x^2 + 5 x = 84

=> x^2 + 5x - 84 = 0

=> x^2 + 12x - 7x - 84 = 0

=> x(x+12) - 7(x+12) = 0

=> (x-7)(x+12) = 0

=> x = 7, -12

=> x = 7 (as length cannot be negative)

=> x+5 = 12

Width, Length = 7 Feet, 12 Feet

Answer 2

Given - Area = 84 square feet

Length of room is 5 feet more than its width

Find - Width and length of room

Solution - As we know, area of rectangle is calculated by multiplying length and width.

Let us assume width of floor to x. Now, as per the question, length of floor is x + 5.

Keeping the values in formula of area of rectangle-

Area = length*breadth

84 = (x + 5)*x

x² + 5x = 84

x² + 5x - 84 = 0

x² + 12x - 7x - 84 = 0

x(x + 12) -7(x + 12) = 0

(x + 12) (x - 7) = 0

Now, the values of x are 7 and -12.

As length can not be negative, x will be 7.

So, width of floor will be 7 square feet.

Length of floor = 5 + 7

Length = 12 square feet.

Hence, width and length of floor = a. 7 feet and 12 feet