+1438 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.
+128474 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
