Respuesta :
The length and width of the rectangle are 19 inches and 13 inches respectively.
Solution:
Given that , A rectangular sheet of metal has an area of 247 square inches. Its perimeter is 64 inches.
Let the length of rectangle be a and width of rectangle be b.
The area of rectangle is given as:
[tex]area = length \times width[/tex]
[tex]\text { Then, area } \rightarrow a b=247[/tex]
The perimeter of rectangle is given as:
Perimeter = 2(length + width)
Then 2(a + b) = 64
a + b = 32 ⇒ (1)
[tex]\begin{array}{l}{\text { Now we know that, }(a-b)^{2}=(a+b)^{2}-4 a b} \\\\ {\text { Then, }(a-b)^{2}=32^{2}-4 \times 247} \\\\ {(a-b)^{2}=1024-988} \\\\ {a-b=\sqrt{36}}\end{array}[/tex]
a – b = 6 ---- (2)
Now solve (1) and (2)
2a = 38
a = 19
Then, 19 + b = 32
b = 32 – 19 = 13
hence, the length and width of the rectangle are 19 inches and 13 inches respectively.
