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​

Answer 1

Working out:

In this question, we are provided with the area of the rectangular graden, and relation between the length & the width of the garden. And we have to find them.

GiveN:

• Area of the graden = 84 ft²
• Length is 5 ft. more than its width.

So, clearly Length > Width in measure.

Let's take Width be x, then length = x + 5

We know,

• Area of rectangle = l × b

Now let's frame a equation based on this formula whose variable in x because length is also expressed in terms of x.

⇛ l × b = 84 ft²

⇛ (x + 5)x = 84

⇛ x² + 5x = 84

⇛ x² + 5x - 84 = 0

Factorising by middle term factorisation,

⇛ x² + 12x - 7x - 84 = 0

⇛ x(x + 12) - 7(x + 12) = 0

⇛ (x + 12)(x - 7) = 0

Then, x = -12 or 7

But length of any side of a rectangle can't be negative, so the value for x = 7 (width), Then length = 12.

So, the correct option is:

$\large{ \boxed{ \bf{ \blue{Option \: A}}}}$

And we are done !!

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Answer 2

Answer :

Let width be x .

According to question,

Length = (x+5) feet

Area = Length × Width

$\sf \longmapsto \large \: x(x + 5) = {x}^{2} + 5x \\ \\ \sf \longmapsto \large \: {x}^{2} + 5x = 84 \\ \\ \sf \longmapsto \large \: {x}^{2} + 5x - 84 = 0 \\ \\ \sf \longmapsto \large \: {x}^{2} + 12x - 7x - 84 = 0 \\ \\ \sf \longmapsto \large \:x(x + 12) - 7(x + 12) = 0 \\ \\ \sf \longmapsto \large \:(x - 7)(x + 12) \\ \\ \sf \longmapsto \large \:x = 7 \: and \: \: - 12$

x = 7 ( As length cannot be negative )

x +5 = 12

•°• Width is 7 feet and length is 12 feet ....

Correct answer is:-

$\bf \boxed{Option (a)}$