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Chapter 6: Q. 327 (page 634)

The area of a bulletin board is 55feet. The length is four feet less than three times the width. Find the length and width of the bulletin board.

Short Answer

Expert verified

The length and width of the bulletin board is 5feetand 11feet.

Step by step solution

01

Step 1. Assumption of integers.

Assume the width and the length of the board to be xfeet,3x-4feet.

Area of bulletin board=length脳width

Substitute the values in the equation of area,

55=x3x-43x2-4x=553x2-4x-55=0......(i)

02

Step 2. Factor the equation.

On factoring,

3x2-15x+11x-55=03xx-5+11x-5=0x-53x+11=0

Use the zero product property,

x-5=0x=5

Then,

3x+11=0x=-113

As we know, the width of the board cannot be negative, so x=5.

Then, the length of the board,

=3x-4=35-4=15-4=11

03

Step 3. Check the answers.

Substitute the width and the length in equation (i),

55=5脳1155=55

This is true.

Hence, the width and the length of the board is5feet,11feet.

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