The length of the diagonal

Question

The width of a rectangle is 9 less than twice it’s length. If the area of the rectangle is 190 cm^2, what is the length of the diagonal?

Answer 1

w = 2l - 9

area = lw = l(2l-9) = 2l^2 -9l = 190

2l^2 - 9l - 190 =0

factor or use the quadratic formula

l = 9 + sqr1609)/4

length = about 12.278

width = 24.556 - 9 = 15.556

use Pythagorean Theorem d^2 = l^2 +w^2

d^2 = 12.278^2 + 15.556^2

d = sqr(12.278^2 + 15.556^2) cm =

length of the diagonal

= about 19.818 centimeters

given rounding errors, d= slightly less than 19.818

Answer 2

For this type of question, we should find the value of the length and width of the rectangle, then use Pythagorean theorem to determine the diagonal.

Step 1: determine the length and width. Using the formula A = LW, we plug in A = 190 cm² and W = 2L -9. This gives us 190 = L(2L-9) as an equation we can use to find the length. Solved, it gives us 12.25 cm as the length. When we use the length to find the width, we get W = 2(12.25) - 9 = 15.5

Step 2: Use the Pythagorean theorem to determine the length of the diagonal, the length and width will be the opposite and adjacent and the diagonal will be our hypotenuse.

diagonal = sqrt((12.25)² + (15.5)²⁾ =19.76cm.

Answer 3