SPECIAL RIGHT TRIANGLES PRACTICE WORKSHEET FOR SAT

Problem 1 :

In rectangle ABCD above, E is on DC, F is on BC, DE = 6 and FC = 1. If the angle A is trisected (divided into three equal angles) by AE and AF, what is the length of BF ?

(a)  5     (b) 5√2 - 1     (c) 5√3-1     (d) 6√3-1

Solution

Problem 2 :

In triangle ABD above, AB = 10, AC = 6 and CD = 8√3. What is the length of BD ?                    Solution

Problem 3 :

In triangle ABC above, the lengths of the sides relate to one another as shown. If the new triangle is created by increasing s by 40 percent and maintaining the relationships among the sides, the area of the new triangle is how many times greater than the area of the triangle ABC ?

(a)  1.16     (b)  1.96      (c)  1.98       (d)  2.16

Solution

Problem 4 :

In the figure above, ACDE is square and ABC is a right triangle. If AB = 3 and BC = 5, what is the length of BD ?

(a)  √53     (b)  √62     (c)  8      (d)  √65

Solution

Problem 5 :

In triangle ABD above, AC = 5 and BD = 10. What is the length of CD ?                      Solution

Problem 6 :

In the figure shown, ΔPQT is a right triangle, and QRST is a square. Find the area of the square, QRST

Solution

Problem 7 :

Using the figure above, we are given that the perimeter of ΔABC is 4 + 2√2. Find the value of y.

Solution

Problem 8 :

Using the figure above, we are given that QRST is a rectangle, and y = 30º. Find the length of RQ.

Solution

Problem 9 :

Given a square with diagonal of length 6, calculate the area of the square.

(a) 9      (b)12       (c) 18       (d) 24      (e)  36

Solution

Problem 10 :

What is the length of AC.

(a) 5√3      (b) 10      (c) 15       (d) 10√3

Solution