a figure is made up of a big square and 4 smaller identical squares. The area of the whole figure is 980 square inches. What is the unknown length?
side of large square --- x
side of smaller square ---- y
x^2 + 4y^2 = 980
x^2 = 980 - 4y^2
x = √(980 - 4y^2)
so 980 - 4y^2 > 0
4y^2 < 980
y^2 < 245
0 < y < appr 15.65 -----> 0 < x < appr 31.3
e.g. suppose y = 7, then x = √(980 - 4(49)) = 28
one large square of 28 by 28, and 4 smaller squares of 7 by 7
Just solve for length.
L=a/w
Either that or you gave too little detail.
no width was given
is there a width provided?
Well, it seems like we've got a mathematical mystery to solve here! Let's start investigating.
Let's call the side length of the big square "x". Since there are four identical smaller squares, we can say that the side length of each smaller square is "y".
So, the area of the big square is x^2, and the area of each smaller square is y^2.
Given that the area of the whole figure is 980 square inches, we can form an equation:
Area of the big square + Area of the four smaller squares = 980
x^2 + 4(y^2) = 980
Now, the problem is asking for the unknown length. Are we referring to the side length "x"? Or the side length "y"?
If we're looking for "x", I'm afraid we'll need more information to solve the equation. But if we're asking for "y", then we can proceed to find its value.
So, which length were you wondering about?
To find the unknown length, we need to set up an equation based on the given information. Let's assume the side length of the big square is "x" inches.
The area of the big square is the side length squared: x^2.
Since there are 4 smaller identical squares, the total area of those squares is 4 times the area of each square. Let's assume the side length of each smaller square is "y" inches.
So, the area of each smaller square is y^2, and the total area of all four squares is 4y^2.
Therefore, the equation we can set up is:
x^2 + 4y^2 = 980
We need to find the unknown length, which is the value of "y". To find it, we need more information or more equations that can be solved simultaneously.