The area of a trapezoid is $80$. The length of one base is $4$ units greater than the other base, and the height of the trapezoid is $12$. Find the perimeter of the trapezoid.

bader Jan 15, 2024

#1**0 **

**We set the smaller base to x, so the area of the trapezoid is**

**\(12x+24 = 80\)**

**\(12x = 56\)**

**\(x = \frac{19}{3}\)**

**Next, we find the diagonals by using pythagorean theorum.**

**a = 2**

**b = 12**

**c = \(\sqrt{148}\) = \(2\sqrt{39}\)**

**so the perimeter is 2x+4+2c = 38/3 + 4 + 4 root 39, or \(\frac{50}{3}+4\sqrt{39}\)**

Imcool Jan 16, 2024