Video: Solving Word Problems Involving Square Roots in a Geometric Context

Mohammed wants to buy fencing to enclose a square garden with an area of 380 ft². How much fencing does he need to buy? Round your answer to the nearest tenth.

03:23

Video Transcript

Mohammed wants to buy fencing to enclose a square garden with an area of 380 feet squared. How much fencing does he need to buy? Round your answer to the nearest tenth.

So, in this question, we know that Mohammed wants to buy fencing to enclose a square garden. So, I’ve drawn a little sketch here of a square garden. And I’ve called each side of the square 𝑥. And we’re told that the area of this garden is 380 feet squared. Okay, so, now what do we need to do to solve the problem?

Well, to solve the problem, we wanna find out how much fencing he needs to buy. But what does that mean in practice? Well, it means that we want to find the perimeter of our square because the fencing is gonna go round the garden. So, it’s gonna be the perimeter of the garden, which is a square as we’ve drawn here. And we can say that the perimeter is equal to four 𝑥. Because it’s gonna be 𝑥 plus 𝑥 plus 𝑥 plus 𝑥, which is four 𝑥. So therefore, what we need to do to work out the perimeter, and hence work out how much fence is needed, is find out the value of 𝑥.

Well, we know that the area of a square can be found by squaring one of the sides. Because it’s 𝑥 multiplied by 𝑥, which is 𝑥 squared. So therefore, we can say that if we wanted to find out one of the side lengths, so in our case, 𝑥, this will be equal to the square root of the area. And that’s because if you square root 𝑥 squared, you get just 𝑥. So, we can say that 𝑥 will be equal to the square root of the area.

So therefore, in our scenario, 𝑥 is gonna be equal to the square root of 380. Now I could work this out but I’m gonna try and keep the accuracy. So, I’ll do that in a bit. Because if we substitute our value for 𝑥 into the formula we had, which was 𝑝 equals four 𝑥, we get p𝑝 the perimeter, is equal to four multiplied by the square root of 380, which gives us a value of 77.9743, et cetera.

Well, we’ve now found the perimeter of our garden. So hence, how much fence is needed to be bought. But have we finished here? Well, no, because if we check back at the question, it wants the answer left to the nearest tenth. So therefore, what I’ve done is I put a line after the tenth. And that’s the nine in our answer here. And then, what I’ve said is that the number next to it, or the digit to the right of it, is our deciding number. Because if this is five or above, it means that we round the nine up.

And because it is five or above, we round the nine up to a ten. And what that means in practice is that our unit will increase by one. And we’ll be left with a zero where the tenths are. So therefore, we can say that if Mohammed wants to buy fencing to enclose a square garden with an area of 380 feet squared, the length of fencing that he’ll need to buy is 78.0 feet. And that’s to one decimal place, or the nearest tenth.

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