Question

The diagonal of a rectangle is 15 cm. The width is 12 cm. What is the length of the rectangle?

Answer 1

Hint: we know that the diagonal, width and length of a rectangle forms a right angles triangle. We have given the 2 sides of this triangle and we need to find the third. So, we will be solving this problem by using Pythagoras theorem.

Complete step by step answer:
Given: Diagonal of the rectangle = 15cm
Width of the rectangle = 12cm.
We have to find the length of the rectangle.
The diagonal, width and length together make a right-angled triangle. So, the diagonal will be the hypotenuse, width will be base and length will be perpendicular.
By using Pythagoras theorem we will find the height of the triangle.
(base)2 + (perpendicular)2 = (hypotenuse)2
Substituting values in the equation. Base is equal to 12cm, hypotenuse is equal to 15cm and we have to find the perpendicular.
${12^2} + {P^2} = {15^2}$
$144 + {P^2} = 225$
${P^2} = 225 - 144$
\[{P^2} = 81\]
Taking square roots on both sides.
$P = \sqrt {81} $
$P = 9$
So, the height of the triangle is 9cm.
Which means that the length of the rectangle is 9 cm.

Note:
A diagonal always divides the rectangle into two congruent right-angled triangles. Two diagonals divide the rectangle into four congruent triangles.
Pythagoras Theorem explains the relation between the sides of a right-angled triangle. It is also sometimes called the Pythagorean Theorem. Pythagoras theorem is basically used to find the length of an unknown side of a triangle. By this theorem, we can derive base, perpendicular and hypotenuse formula. Which is hypotenuse² = perpendicular² + base².