# Find the sides of a rectangle whose perimeter is equal to the perimeter of a triangle with sides of

June 27, 2021 | education

| **Find the sides of a rectangle whose perimeter is equal to the perimeter of a triangle with sides of 9cm, 4cm, and 7cm, Try to find different solutions, the lengths of the sides of the rectangle**

Find the perimeter of a given triangle:

P = 9 + 4 + 7 = 20 cm.

Let us denote the width of the required rectangle by a and the length by b. Let’s write down the formula for its perimeter:

P = 2 * (a + b);

a + b = P / 2;

a + b = 20/2 = 10.

Knowing that a, b are positive integers and add up to 10, we compile a table of all possible sizes of rectangles:

a (cm) 1 2 3 4 5 b (cm) 9 8 7 6 5

Answer: the conditions are met by rectangles with dimensions: 1 cm and 9 cm; 2 cm and 8 cm; 3 cm and 7 cm; 4 cm and 6 cm; 5 cm and 5 cm.

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