Question

The length of a rectangle is twice the width. The area of the rectangle is 90 square units. Note that you can divide the rectangle into two squares. a. Which irrational number represents the length of each side of the squares? Area 90 square units b. Estimate the length and width of the rectangle.

Answer 1

we know that

The area of a rectangle is giving by the formula

A=LW

where

L is the length

W is the width

In this problem we have

A=90 units^2

L=2W ------> The length of a rectangle is twice the width

substitute

90=(2W)W

solve for W

90=2W^2

W^2=45

take square root both sides

W=6.7 units

Find the value of L

L=2W

L=2(6.7)=13.4 units

The approximate length is 13.4 units and the width is 6.7 units

the exact value of the length and with are

$W=\sqrt{45\text{ units}}$

simplify

$W=3\sqrt{5\text{ units}}$

The length is

$L=6\sqrt{5\text{ units}}$

The irrational number that represents the length of each side of the squares is equal to the width

so

$3\sqrt{5\text{ units}}$