Chapter 11.1, Problem 3PSA

a

To determine

To find : The area of a rectangle with given side and diagonal

Answer to Problem 3PSA

The area is $A=120$

Explanation of Solution

Given information : The following information has been given

The diagonal of rectangle $d=17$

The length of the rectangle $l=8$

Formula used : The area of any rectangle will be

  $A=(lengt{h}_1)(widt{h}_1)$

Calculation : we calculate the width of the rectangle from the half right triangle as

  $w=\sqrt{{17}^2-8^2}=15$

We know that the area of any rectangle will be

  $A=(length)(width)$

Hence, substituting the values from the given information, we get

  $A=(8)(15)=120$

Thus, we get

  $A=120$

b

To determine

To find : The area of a rectangle with given side and perimeter

Answer to Problem 3PSA

The area is $A=72$

Explanation of Solution

Given information : The following information has been given

The perimeter of rectangle $P=40$

The length of the rectangle $l=6$

Formula used : The area of any rectangle will be

  $A=(lengt{h}_1)(widt{h}_1)$

Calculation : we calculate the width of the rectangle from the perimeter as

  $P=2(l+w)=40=2(6+w)\to w=12$

We know that the area of any rectangle will be

  $A=(length)(width)$

Hence, substituting the values from the given information, we get

  $A=(6)(12)=72$

Thus, we get

  $A=72$