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Chapter 6: Q. 326 (page 627)

A rectangular retaining wall has area 15square feet. The height of the wall is two feet less than its length. Find the height and the length of the wall.

Short Answer

Expert verified

The height and the length of the wall is 3feetand 5feet.

Step by step solution

01

Step 1. Assumption of integers.

Assume the length to be xfeetand height of the wall to be localid="1644680828723" x-2feet.

Area of rectangular retaining wall=length脳height

Substitute the values in the equation of area,

15=x-2xx2-2x=15x2-2x-15=0......(i)

02

Step 2. Factor the equation.

On factoring,

x2-5x+3x-15=0xx-5+3x-5=0x-5x+3=0

Use the zero product property,

x-5=0x=5

Then,

x+3=0x=-3

As we know, the length of the wall cannot be negative, so x=5.

Then, the height of the wall=x-2=5-2=3

03

Step 3. Check the answers.

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

15=3脳515=15

This is true.

Hence, the height and the length of the wall isrole="math" localid="1644681261849" 3feetand5feet.

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