X, Y and Z are three equilateral triangles. The sum of the areas of X and Y is equal to the area of Z. If the side lengths of X and Y are 6 cm and 8 cm respectively, then what is the side length of Z?

Explanation

Area of an equilateral triangle is \frac{\sqrt{3}}{4}a^2. The sum of areas is \frac{\sqrt{3}}{4}(6^2) + \frac{\sqrt{3}}{4}(8^2) = \frac{\sqrt{3}}{4}(z^2). This simplifies to 36 + 64 = z^2 \implies z^2 = 100 \implies z = 10\text{ cm}.

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...