what kind of rectangle has an area of 10 square units and a perimeter of 14 units?

Question

need to draw a picture of the rectangle

Answer 1

Given rectangle area is 10 squre units.

lb = 10

b = 10/l

Perimeter is 14 units.

2(l+b) = 14

Divide to each side by 2.

2(l+b)/2 = 14/2

l+b = 7

Substitute the b value in l+b = 7

l+10/l = 7

(l^2+10)/l = 7

Multiple to each side by l.

(l^2+10)l/l = 7l

l^2+10 = 7l

Subtract 7l from each side.

l^2+10-7l = 7l-7l

l^2-7l+10 = 0

l^2-5l-2l+10 = 0

l(l-5)-2(l-5) = 0

(l-2)(l-5) = 0

l-2 = 0, l-5 = 0

l = 2, l = 5

For l = 2, b = 10/2 = 5

For l = 5, b = 10/5 = 2

Always length is greater than width of a rectangle.

So the dimensions of given rectangle is l = 5units and width is b = 2units.