# The width and length of a rectangle is equal to 7:13, and its half-perimeter is 180 cm. Find the area of a square

The width and length of a rectangle is equal to 7:13, and its half-perimeter is 180 cm. Find the area of a square if its side is 2/9 of the length of this rectangle.

Suppose that the width of our rectangle is X cm, and its length is Y cm.
Considering that the semi-perimeter is the sum of the width and length, we get:
X + Y = 180
X: Y = 7: 13
Let’s solve the resulting system by expressing one of the variables through the other, i.e.
X = 180 – Y
(180 – Y): Y = 7: 13
180 / Y – 1 = 7/13
180 / Y = 20/13
Y = 117, i.e. length – 117 cm,
180 – 117 = 63, i.e. width – 63 s).
Determine the side of the square: 117 * 2/9 = 26 (cm).
The area of the required square: 26 * 26 = 676 (cm2).

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