One side of the rectangle is 12 cm larger than the other. Find the sides of a rectangle if its area is 405cm2.

Rectangle;

Width – ? cm;

Length – ? 12 cm wider;

Area – 405 cm ^ 2.

Solution:

Let’s introduce the variables: let x cm – the width of the rectangle, y cm – its length.

Based on the available data, we will compose the equations of the system. Since the length is 12 cm larger than the width, it means: y – x = 12.On the other hand, the area of ​​a rectangle is equal to the product of its width and length: x * y = 405.

We got a system of equations: {x – y = 12, x * y = 405. Let’s solve it by the substitution method, expressing from the first equation x = y + 12, and substituting it into the second:

(y + 12) * y = 405;

y ^ 2 + 12y – 405 = 0;

D = 12 ^ 2 – 4 * 1 * (-405) = 1764;

y1 = (-12 + √1764) / 2 = 15 (cm) – width;

y2 = (-12 – √1764) / 2 = -27 – width cannot be negative.

x = 15 + 12 = 27 (cm) – length.

Answer: 15 cm and 27 cm.