Question

The area of a rectangular trampoline is 135 ft2. The length of the trampoline is 6 ft greater than the width of the trampoline. This situation can be represented by the equation w2+6w−135=0.

What is the width of the trampoline, in feet?

Question 7 options:

15 feet


5 feet


6 feet


9 feet

Answer 1

• 9 feet.

Explanation :

Given :

• The area of a rectangular trampoline is 135 ft².
• The length of the trampoline is 6 ft greater than the width of the trampoline.

To find :

• The width of the trampoline.

Solution :

Let us assume the width of the rectangle as w and therefore the length becomes (w + 6) .

We know that,

`{ \qquad \dashrightarrow \bf{Length * Width =Area _((rectangle)) }}`

Substituting the values in the formula :

`{\qquad \sf \dashrightarrow (w + 6)w = 135}`

`{\qquad \sf \dashrightarrow {w}^(2) + 6w = 135}`

`{\qquad \sf \dashrightarrow {w}^(2) + 6w - 135 = 0}`

`{\qquad \sf \dashrightarrow {w}^(2) + 15w - 9w - 135 = 0}`

`{\qquad \sf \dashrightarrow {w}(w + 15) - 9(w + 15) = 0}`

`{\qquad \sf \dashrightarrow (w + 15) (w - 9) = 0}`

`{\qquad \sf \dashrightarrow (w + 15) = 0}`

`{\qquad \sf \dashrightarrow w = - 15}`

`{\qquad \sf \dashrightarrow (w - 9) = 0}`

`{\qquad \sf \dashrightarrow w = 9}`

• Whether, w = (– 15) or 9 .

The width of the rectangle cannot be negative therefore the width of the rectangle must be 9 feet .

Answer 2

`\bold{\huge{\blue{\underline{ Solution }}}}`

Given :-

• The area of rectangular trampoline is 135ft².
• The length of the trampoline is 6ft greater than the width of the trampoline .

To Find :-

• We have to find the width of the trampoline

Let's Begin :-

We have,

• Area of rectangular trampoline = 135ft²

Let the width of the rectangular trampoline be w

According to the question,

• Length is 6ft greater than width

Therefore,

The length of the rectangular trampoline will be

`\sf{ = (W + 6 )ft }`

Now,

We know that,

`\bold{\blue{ Area\: of\: rectangle = Length × Breath }}`

Subsitute the required values,

`\sf{ 135 = w(w + 6 ) }`

`\sf{ 135 = w² + 6w}`

`\sf{ = w² + 6w - 135 }`

By factorization method,

`\sf{ = w² - 9w + 15w - 135 }`

`\sf{ = w( w - 9) + 15( w - 9)}`

`\sf{ = ( w + 15) ( w - 9)}`

Therefore,

Width of the rectangular trampoline

`\sf{ w = - 15 \: or\: w = 9 }`

[ Width of the rectangle can never be negative ]

Thus , The width of the rectangular trampoline is 9 feet

`\bold{\pink{ Hence\:, Option \:D\: is\: correct }}`