Respuesta :

P=2a+2b=2(a+b),         Area=a*b
diagonal=d
d²=a²+b²

92=2(a+b)---->    46=a+b ------>a=46-b
34²=a²+b² ----->    34²=(46-b)²+b²
34²=(46-b)²+b²
1156=2116-92b+b²+b²
2b²-92b+960=0
b²-46b+480=0
D=46²-4*480=
b=(46+/-√(46²-4*480))/2,
b=(46+/-√196)/2, we take only b=(46+√196)/2=(46+14)/2=60/2=30
b=30
a=46-b=46-30=16
a=16
A=a*b=30*16=480 ft²



Cricetus

The area of the rectangle will be "480 ft²".

Given,

  • Perimeter = 92 feet
  • Diagonal = 34 feet

We know that,

→ [tex]d^2 = a^2 +b^2[/tex]

By putting the values, we get

  [tex]34^2 = (46-b)^2 +b^2[/tex]

[tex]1156 = 2116-92 b+b^2+b^2[/tex]

 [tex]2b^2-92 b +960 =0[/tex]

   [tex]b^2-46 b+480 =0[/tex]

                        [tex]b = \frac{(46+ \sqrt{196} )}{2}[/tex]

                           [tex]= \frac{46+14}{2}[/tex]

                           [tex]= 30[/tex]

Now,

→ [tex]a = 46-b[/tex]

     [tex]= 46-30[/tex]

     [tex]= 16[/tex]

hence,

The area of rectangle,

→ [tex]A = a\times b[/tex]

      [tex]= 30\times 16[/tex]

      [tex]= 480 \ ft^2[/tex]

Thus the above answer is right.    

Learn more about area here:

https://brainly.com/question/13468587

Otras preguntas