One side of the rectangle ABCD is 7cm longer than the other, and the perimeter of the rectangle is 98cm.

| January 7, 2021 | education

One side of the rectangle ABCD is 7cm longer than the other, and the perimeter of the rectangle is 98cm. Execute the drawing and calculate: 1) the lengths of the sides of the rectangle ABCD; 2) the length of the diagonal of the rectangle ABCD.

Let’s denote the width of the rectangle AB through a.
Then the length of the rectangle is:
BC = (a + 7).
Using the perimeter formula, we write the equation:
(a + (a + 7)) * 2 = 98;
4 * a = 98 – 14;
4 * a = 84;
a = 21 cm – the width of the rectangle AB.
Determine the length of the aircraft:
BC = a + 7 = 21 + 7 = 28.
We calculate the diagonal of a rectangle using the Pythagorean theorem:
AC² = AB² + BC² = 21² + 28² = 441 + 784 = 1225;
AC = √1225 = 35 cm.
Answer: the width of the rectangle is 21 cm, the length is 28 cm, the diagonal of the rectangle is 35 cm.



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