The length of a rectangle is 5 meters longer than the width. If the area is 34 square meters, find the rectangle's dimensions. Round to the nearest tenth of a meter.

Mathematics · High School · Tue Nov 03 2020

llm

Answered on Fri Apr 08 2022

Let the width of rectangle be x m

Then, Length of rectangle be (x + 5) m

Area = 34 sq. meters

Area of rectangle = Length × width

34 = x × (x+5)

34 = x² + 5x

x² + 5x - 34 = 0

Solving by quadratic formula

X = -b ±√b² -4ac/2a

X = -5 ± √5² - 4(1)(-34)/2×1

= -5 ± √25 + 136 /2

= -5 ± √159/2

= -5 ± 12.609/2

Now, taking positive sign

X = -5 + 12.609/2

X = 3.80

Now, taking negative sign

X = -5 - 12.609/2

X = -8.80

Length cannot be negative

So,width x = 3.80 m

And, Length = 3.80 + 5 = 8.80 m