All SAT Math Resources
Example Question #202 : Sat Mathematics
The two rectangles shown below are similar. What is the length of EF?
When two polygons are similar, the lengths of their corresponding sides are proportional to each other. In this diagram, AC and EG are corresponding sides and AB and EF are corresponding sides.
To solve this question, you can therefore write a proportion:
AC/EG = AB/EF ≥ 3/6 = 5/EF
From this proportion, we know that side EF is equal to 10.
Example Question #31 : Quadrilaterals
A rectangle is x inches long and 3x inches wide. If the area of the rectangle is 108, what is the value of x?
Solve for x
Area of a rectangle A = lw = x(3x) = 3x2 = 108
x2 = 36
x = 6
Example Question #1 : How To Find The Length Of The Side Of A Rectangle
If the area of rectangle is 52 meters squared and the perimeter of the same rectangle is 34 meters. What is the length of the larger side of the rectangle if the sides are integers?
Area of a rectangle is = lw
Perimeter = 2(l+w)
We are given 34 = 2(l+w) or 17 = (l+w)
possible combinations of l + w
are 1+16, 2+15, 3+14, 4+13... ect
We are also given the area of the rectangle is 52 meters squared.
Do any of the above combinations when multiplied together= 52 meters squared? yes 4x13 = 52
Therefore the longest side of the rectangle is 13 meters
Example Question #2 : How To Find The Length Of The Side Of A Rectangle
Figure is not drawn to scale.
The provided figure is a rectangle divided into two smaller rectangles, with
Rectangle Rectangle .
Which expression is equal to the length of ?
Since Rectangle is similar to Rectangle , it follows that corresponding sides are in proportion. Specifically,
since , if we let , then
Setting , , and , the proportion statement becomes
Cross-multiplying, we get
Simplifying, we get
Since this is quadratic, all terms must be moved to one side:
The solutions to quadratic equation
can be found by way of the quadratic formula
Simplifying the radical using the Product of Radicals Property, we get
Splitting the fraction and reducing:
This actually tells us that the lengths of the two segments and have the lengths and . is seen in the diagram to be the longer, so we choose the greater value, .