Chapter ISG, Problem 8.9STP

To determine

To find figure having greater area

Answer to Problem 8.9STP

Square has greater area.

Explanation of Solution

Given information:

Two figures: square and rectangle

Side of square= $x$

Length of rectangle= $x+1$

Breadth of rectangle= $x-1$

Formula used:

  Area of square= ${(side)}^2$

  Area of rectangle= $length\times breadth$

Calculation:

For area of square, substituting values,

  Area= ${(x)}^2$

For area of rectangle, substituting values

  Area= $(x+1)(x-1)$

Solving using identity,

  Area= $x^2-1^2$

Hence, area of square is greater than area of rectangle.

Putting $x$ =4

  Area of square= $4^2$

Hence, area of square is 16 unit²

  Area of rectangle= $4^2-1^2$

Solving,

  Area =16-1

Hence, area of rectangle is 15 unit²

Putting $x$ =7

  Area of square= $7^2$

Hence, area of square is 49 unit²

  Area of rectangle= $7^2-1^2$

Solving,

  Area =49-1

Hence, area of rectangle is 48 unit²