Question

the length of a rectangle is 5 meters longer than the width. if the area is 23 square meters, find the rectangles dimensions. round to the nearest tenth of a meter

Answer 1

The rectangle is 7.9 meters by 2.9 meters.

Explanation:

Let l be the length and w be the width

l = w + 5

A = 23 m²

Formula: A = lw

Solve for the dimensions

23 = (w+5)w

23 = w² + 5w

w² + 5w - 23 = 0

Use quadratic formula to find the possible value/s of w

`w = (-b+-√(b^2-4ac) )/(2a)\\ w = (-5+-√(5^2-4(1)(-23)) )/(2(1)) \\w = (-5+-√(25+92) )/(2)\\ w = (-5+-√(117) )/(2) \\w = (-5+-√(9(13)) )/(2) \\w = (-5+-3√(13) )/(2)\\ w = (-5+3√(13) )/(2) = 2.9\\ w = (-5-3√(13) )/(2) = -7.9`

Since we're dealing with dimensions, take the positive value which is 2.9.

w = 2.9 m

Substitute the value to l = w + 5

l = 2.9 + 5

l = 7.9 m