Chapter 11.1, Problem 4PSA

a

To determine

To find : The base length of a rectangle with given area and altitude

Answer to Problem 4PSA

The base length is $b=8\text{ mm}$

Explanation of Solution

Given information : The following information has been given

The area of rectangle $(A)=48{\text{ mm}}^2$

The altitude of the rectangle $(a)=6\text{ mm}$

Formula used : The area of any rectangle will be

  $A=(lengt{h}_1)(widt{h}_1)$

Calculation : We know that the area of any rectangle will be

  $A=(base)(altitude)$

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

  $48{\text{ mm}}^2=(b)(6\text{ mm})$

Thus, we get

  $b=8\text{ mm}$

b

To determine

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

Answer to Problem 4PSA

The diagonal length is $d=10\text{ mm}$

Explanation of Solution

Given information : The following information has been given

The area of rectangle $A=48{\text{ mm}}^2$

The altitude of the rectangle $a=6\text{ mm}$

The base length is $b=8\text{ mm}$

Formula used :

Pythagoras theorem

  $a=\sqrt{(b^2)+{(c)}^2}$

Where

“ a ” is the hypotenuse of the right-angle triangle

“ b ” is the base of the right-angle triangle

“c” is the perpendicular of the right-angle triangle

Calculation :

We calculate the diagonal of the rectangle from the sides by using Pythagoras theorem

  $\begin{array}{l}d=\sqrt{(6{\text{ mm}}^2)+{(8\text{ mm})}^2}\\ d=10\text{ mm}\end{array}$

Thus, we get

  $d=10\text{ mm}$