In the figure below, PQRS is a parallelogram of perimeter 24 and area 28. What is the perimeter of rectangle QOST? Include an explanation of how you solved the problem.
If the permeter of PQRS is 24....remember that PQ = SR and PS = QR
So...... PQ + SR + PS + QR = 24
5 + 5 + PS + QR = 24 sub PS for QR
10 + PS + PS = 24 subtract 10 on each side
2PS = 14 divide both sides by 2
PS = 7 = QR
And the area of PQRS = PS * height of PQRS (=ST) ......so we have that
28 = 7 * ST divide both sides by 7
4 = ST
And since RST is a right triangle.... using the Pythagorean Theorem...
RS^2 - ST^2 = RT^2
5^2 - 4^2 = RT^2
25 - 16 = RT^2
9 = RT^2 take the square root of both sides
3 = RT
So........QT = QR + RT = PS + RT = 7 + 3 = 10
So...the perimeter of QOST = 2 [ QT + ST] = 2 [ 10 + 4] = 2 * 14 = 28