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# Ramesh wants to build a fence around the right angled triangular garden in his backyard. The perpendicular sides of the garden are measured and found to be $2 m$ and $1m$ long. He goes to the local store to buy the fencing. What is the perimeter of the garden in meters? When he went to the store, he came to know that the store sells fencing in tenths of a meter i.e. decimetre. Thus what length of fencing should Ramesh ask for?

Last updated date: 13th Sep 2024
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Hint: First of all we have to look for the geometry of the region to be considered (here, ground) and draw the rough sketch in order to visualize the problem. Here the shape of the ground is triangular.

Complete step by step solution:
So, let the figure shown in the diagram below represent the garden.

Then we have to look for the information given about the corresponding region such as dimensions, area or perimeter. Here, the lengths of the perpendicular sides (i.e. legs) are given in question. Now, we have to identify the parameter (area, perimeter or dimensions) which needs to be calculated in order to solve the given problem.
Here, we have to calculate the perimeter of the ground.
Then, we have to use the known formula or expression and look for the unknowns which are required to put in the formula.
So the formula we will use is:
Perimeter of triangular garden = AB + BC + AC
Where we don’t know the length of AC.
Then, try to find the unknowns from the given information.
Here the length of AC can be calculated using the Pythagoras’ theorem.
$\Rightarrow AC = \sqrt {A{B^2} + B{C^2}} = \sqrt {{1^2} + {2^2}} = \sqrt 5 {\text{ }}m$
Thus,
Perimeter of triangular garden = AB + BC + AC = $1 + 2 + \sqrt 5 = 3 + \sqrt 5 \approx 3 + 2.24 \approx 5.24{\text{ }}m$
Now, it is given that the store sells the fence in tenth of a metre. Which means the smallest unit that can be measured at store is 0.1 metre. Thus, stores can sell fences of lengths $0.1, 0.2, 0.3, 0.4$ and so on. The perimeter of the ground is 5.24 m. But the store can sell fences of length $5.2m$ or $5.3m$. Thus Ramesh should ask for the fencing of length 5.3 m. in order to avoid the shortage.

Note: Here rounding off the length to the nearest first decimal place will give $5.2 m$ as the answer. But the length of the fence is more than that. Thus to avoid the shortage of fence, Ramesh should ask for the fencing of length $5.3 m$.