Question

The floor of a truck is 24 cm above the ground. The ramp
attached to the back of the truck touches the ground at a point which is
10 cm away from the truck.What is the length of the ramp?

Answer 1

Given:

• Height of the floor of truck above ground level = $24cm$

• Distance between the truck and the point where the ramp attached to the back of truck touches the ground = $10cm$

To find:

Length of the ramp attached to the back of truck.

Note:

An image is attached showing the figure which indicates the situation, along with the dimensions given.

Formula to be used:

• Form the figure, it can be understood that the situation can be explained as a right angled triangle.
• Pythagoras theorem, which gives the relation between the hypotenuse and the sides of a right angled triangle, can be used for the calculation of length of the ramp of the truck.
• From the figure (in image), Pythagoras theorem is given by:

$BC^{2}=AB^{2}+AC^{2}$

• Let the length of hypotenuse be '$x$'.

⇒$x^{2}=AB^{2}+AC^{2}$.....(1)

Solution:

• The height of truck's floor is: $AC=24cm$

• The distance of the point  where the ramp touches the ground, from the truck is: $AB=10cm$

• Now, using equation (1), the length of ramp ($x$) is calculated in the following way:

$x^{2}=AB^{2}+AC^{2}\\x^{2}=10^{2}+24^{2}\\x^{2}=100+576\\x^{2}=676\\x=\sqrt{676}\\ x=26cm$

⇒The length of ramp of the truck is $26cm$.

Final Answer:

The length of the ramp attached to the back of truck is $26cm$.