Name: Triangle Inequality Theorem
Uploaded: 2019-07-19
Duration: 5 min 58 s
Description: Measure the sum of lengths of two sides of a triangle and you'll find it to be greater than the length of the other side. Learn more about triangle inequalit...

Question

A ladder $45 f t$ tall when set against a wall of a house, just reaches the window at a height of $27 f t$ . How far is the lower end of the ladder from the base of the wall?

Accepted Answer

When the ladder is sent against the wall then the ladder and the wall and the ground form a right-angled triangle.

With hypotenuse (ladder) $= 45 c m$

Opposite side(height at the window) $= 27 c m$

Pythagoras theorem states that 'In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides'. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle $90 °$ .

Let the base be $x$ .

Now, by the theorem we know;

$H y p o t e n u s e^{2} = P e r p e n d i c u l a r^{2} + B a s e^{2}$

$45^{2} = 27^{2} + x^{2}$

$x^{2} = 45^{2} - 27^{2}$

$x^{2} = 2025 - 729$

$x^{2} = 1296$

$x = \sqrt{1296}$

$x = 36 c m$

Hence, the lower end of the ladder is $27 f t$ far from the base of the wall.

A ladder $45 f t$ tall when set against a wall of a house, just reaches the window at a height of $27 f t$ . How far is the lower end of the ladder from the base of the wall?

Important Questions on Triangles

Learn and Prepare for any exam you want !

A ladder 45 ft tall when set against a wall of a house, just reaches the window at a height of 27 ft. How far is the lower end of the ladder from the base of the wall?

Important Questions on Triangles

Learn and Prepare for any exam you want !

A ladder $45 f t$ tall when set against a wall of a house, just reaches the window at a height of $27 f t$ . How far is the lower end of the ladder from the base of the wall?