Question

14. The area of a rectangle is 375 square inches and it’s perimeter is 80 inches. Find both the length and width.

Answer 1

Answer:

Length  $=25$ inches

Width $= 15$ inches

Step-by-step explanation:

Let $l$ = length of rectangle, $w$ = width of rectangle

Given the area and the perimeter of the rectangle, we can write:

$lw = 375$

$2l+2w=80$

So:

$l+w = 80\div2$

$=40$

$l=40-w$

Now, we can use substitution to find the value of $w$:

$lw = 375$

$(40-w)w = 375$

$40w-w^2 = 375$

$375+w^2-40w = 0$ (Quadratic equation)

$(w-15)(w-25) = 0$

∴ $w = 15, 25$

We can use substitution again to find the value of $l$

$lw = 375$

$l=375\div w$

$=25,15$

∵ Length usually refers to the longer side of a rectangle, ∴ length $=25$ inches and width $=15$ inches.

Hope this helps :)