# Find the length of the rectangle if the width and diagonal of the rectangle is 3cm and 5cm.

January 17, 2021 | education

| We are given a rectangle with a width and diagonal of 3 cm and 5 cm, respectively. To find the length of a rectangle, we will consider a right-angled triangle formed by the sides of the triangle and the diagonal.

The unknown side of the rectangle is the leg of the right-angled triangle. Let us apply the Pythagorean theorem for this.

c ^ 2 = a ^ 2 + b ^ 2.

a ^ 2 = c ^ 2 – b ^ 2.

a = √ (c ^ 2 – b ^ 2).

We substitute the values into the formula and perform calculations:

a = √ (5 ^ 2 – 3 ^ 2) = √ (25 – 9) = √16 = 4 cm rectangle length.

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