Answer :
Answer:
She should make a rectangle with dimensions 14.4 cm by 4.2 cm.
Step-by-step explanation:
- The diagonal of a rectangle is represented by [tex]\sqrt{length^2+width^2}[/tex].
- Area of rectangle is = length×width
- Perimeter of a rectangle = 2(length+width).
Assume x be the width of the rectangle.
The length of the rectangle is to be 6 cm more than twice the width.
The length of the rectangle is= (2x+6) cm
Then the diagonal of the rectangle is [tex]\sqrt{length^2+width^2}[/tex]
[tex]=\sqrt{(2x+6)^2+x^2}[/tex]
[tex]=\sqrt{4x^2+24x+36+x^2}[/tex]
[tex]=\sqrt{5x^2+24x+36}[/tex] cm
According to the problem,
[tex]\sqrt{5x^2+24x+36}=15[/tex]
Squaring both sides
[tex]\Rightarrow{5x^2+24x+36}=15^2[/tex]
[tex]\Rightarrow{5x^2+24x+36}=225[/tex]
[tex]\Rightarrow{5x^2+24x+36-225=0[/tex]
[tex]\Rightarrow{5x^2+24x-189=0[/tex]
⇒5x²+45x-21x-189=0
⇒5x(x+9)-21(x+9)=0
⇒(x+9)(5x-21)=0
⇒x+9=0 or, 5x-21=0
[tex]\Rightarrow x=-9, \frac{21}5[/tex]
⇒x= -9, 4.2
Since the width of a rectangle can not negative.
So, x=4.2 cm
The width of rectangle is = 4.2 cm
The length of the rectangle is =(2×4.2+6)
=14.4 cm
She should make a rectangle with dimensions 14.4 cm by 4.2 cm.