What is the area of the square?
Consider the following for the next three (03) items that follow:<br>A triangle CEF is drawn inside a square ABCD as shown in the figure given below. Given: CF=8 cm, EF=6 cm and CE=10 cm.
- A. \frac{512}{17} square cm
- B. \frac{625}{13} square cm
- C. \frac{1024}{17} square cm ✓
- D. \frac{1296}{13} square cm
Correct Answer: C. \frac{1024}{17} square cm
Explanation
Let the side of the square be a. Using the Pythagorean theorem in the three right triangles at the corners, BF = \sqrt{64-a^2} and DE = \sqrt{100-a^2}. The remaining segments on the sides form the third right triangle: (a - \sqrt{100-a^2})^2 + (a - \sqrt{64-a^2})^2 = 6^2. Solving this yields a^2 = \frac{1024}{17}. The area is a^2.
Related questions on Geometry
- In a triangle ABC, \angle A = 30^\circ, AB = 7 cm and AC = 12 cm. What is the area of the triangle ABC?
- ABC is a triangle right angled at B. D is a point on AC such that BD is perpendicular to AC. If AB = p and BC = \sqrt{3}p, then what is BD...
- The difference between an interior angle and an exterior angle of a regular polygon is 120°. What is the number of sides of the polygon?
- An angle q is exactly one-fourth of its complementary angle. What is the value of angle q?
- The sides of a triangle are 11 cm, 60 cm and 61 cm. What is the area of the triangle formed by joining the mid-points of the sides of the tr...