Question

Eighth grade

Answer 1

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:

$area = length \times width$

$\text { Then, area } \rightarrow a b=247$

The perimeter of rectangle is given as:

Perimeter = 2(length + width)

Then 2(a + b) = 64

a + b = 32 ⇒ (1)

$\begin{array}{l}{\text { Now we know that, }(a-b)^{2}=(a+b)^{2}-4 a b} \\\\ {\text { Then, }(a-b)^{2}=32^{2}-4 \times 247} \\\\ {(a-b)^{2}=1024-988} \\\\ {a-b=\sqrt{36}}\end{array}$

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.