Solve each problem. See Examples 1 and 2. Dimensions of a Square....

Question

Solve each problem. See Examples 1 and 2. Dimensions of a Square. The length of each side of a square is 3 in. more than the length of each side of a smaller square. The sum of the areas of the squares is 149 in.2. Find the lengths of the sides of the two squares.

Accepted Answer

Hello, everyone in this video, we're going to be looking at this practice problem where we want to figure out the side lengths of two squares and were given some characteristics about them. We know that there are different sizes and the total area of both of them together is 194 ft squared. And the side of the larger square is eight ft longer than the other one. So when we're talking about a square recall that all of the links are the same. So say I call this link A, that means that length A is the same for all four sides. So let's say I call this length B for the bigger squared, then the links are the same for all the sides. And one of the things that we know is that when we take the total area of both of these squares, so if I did A squared plus B squared, That is equal to 194 beats squared. But in this equation, you can see that we have two variables a and B so we can't solve for either of them. So we need to find a way to relate the two variables. Well, we're also given that the larger square is eight ft longer than the other one. So that means that the length for B is equal to the length of the smaller, the smaller square a plus eight ft. So now I can substitute a plus eight for B in my equation. And if I do that, I have a squared plus A plus eight squared is equal to 194. And now I only have to solve for the variable A. So if I do that, I'm going to start by expanding a plus eight times a plus eight, still equal to 194. So I'll do the foil method or I have a times A is A squared, A times eight is eight A and again, eight times A is eight A, then I have eight times eight is 64. I can combine these middle terms eight A plus eight A is 16 A and that's still equal to 1 94. I can also combine these first two terms A squared plus A squared is two A squared. And I'm going to go ahead and move the 194 over to the left hand side by subtracting By 194. So it leaves me with two A squared plus 16 A and 64 -1 94 is equal to negative one 30. And now my right hand side is zero and I'm actually going to divide this entire equation by two to try to get rid of this coefficient. So when I do that two A squared divided by two is a squared 16 A divided by two is eight A and negative 1 30 divided by two is negative 65. And my right hand side is zero, divided by two, which still gives me zero. And now you can see that we have a sort of quadratic equation here. So I'm going to try to solve for a by factoring. So in my two factors, my first terms need to multiply to give me a squared. So two terms that I can think of that multiply two A squared is A times A and my second terms need to multiply to give me negative 65. So when I think of factors of negative 65 I can do one and 65 or and five. And I want my factors to give me a difference of positive eight. That means probably want the five to be negative because 13 minus five gives me positive eight and 13 times negative five gives me negative 65. So I can have a plus 13 and a -5 as my two factors. And once I have these two factors I can solve for a because I can have a plus 13 is equal to zero. So in this factor a equals negative Or I could have a -5 is equal to zero. So when I saw for a here, a is equal to positive five. So in this case, we're talking about lengths. So a negative length doesn't really make sense. So I'm going to eliminate a equals negative 13 as an answer and say that a is equal to five. That means that The length of the smaller square is five ft. And I determined the relationship to find the length of the bigger square. As I said, the length of the bigger square B is equal to A. So five plus eight, which is equal to 13. So that means that for the bigger length, this is 13 ft. That means that my links are five ft and 13 ft. So this becomes my final answer for this problem. And you can see that answer choice. A also has five ft and 13 ft. So hopefully this video helped and see you next time.

Solve each problem. See Examples 1 and 2. Dimensions of a Square. The length of each side of a square is 3 in. more than the length of each side of a smaller square. The sum of the areas of the squares is 149 in.2. Find the lengths of the sides of the two squares.

Key Concepts

Area of a Square

Algebraic Expressions

System of Equations

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