SOLUTION: In two square plots of grass, a side of one is ten yards longer than the side of the other, and areas are as 25 to 9. What are lengths of sides? A square has equal sides. Ar

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Question 1133936: In two square plots of grass, a side of one is ten yards longer than the side of the other, and areas are as 25 to 9. What are lengths of sides?
A square has equal sides.
Area of square = x^2

Let squares be square a and square b.
b = a + 10
Not sure how to continue.
Found 3 solutions by josgarithmetic, MathTherapy, greenestamps:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
small plot x by x
Large plot x+10 by x+10

%28x%2B10%29%5E2%2Fx%5E2=25%2F9
.
.
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Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

In two square plots of grass, a side of one is ten yards longer than the side of the other, and areas are as 25 to 9. What are lengths of sides?
A square has equal sides.
Area of square = x^2

Let squares be square a and square b.
b = a + 10
Not sure how to continue. 
If each side of the smaller square is "a," as you indicated, then each side of the larger square = a + 10

We then get: matrix%281%2C3%2C+a%5E2%2F%28a+%2B+10%29%5E2%2C+%22=%22%2C+9%2F25%29

Solve this for "a," a side of the smaller square, and you should get a length of highlight_green%28matrix%281%2C2%2C+15%2C+yards%29%29. 

Add 10 to that to get highlight_green%28matrix%281%2C2%2C+25%2C+yards%29%29 as the length of each side of the larger square.

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


All squares are similar. The ratio of areas of any similar figures is the square of the ratio of the linear measurements of the figures. If the ratio of areas is 25:9, then the ratio of side lengths is 5:3.

It is given that the side of one square is 10 yards more than the side of the other.

Using the ratio 5:3 of the side lengths, let the sides of the two squares by 5x and 3x. Then their difference is 2x; and we know the difference between the two side lengths is 10. So 2x=10 --> x=5; and then the two side lengths are 3x=15 and 5x=25.