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?

Question

Question

This question was previously asked in

SSC CHSL Tier-I Exam 2022 Official Paper (Held On: 13 March, 2023 Shift 2)

Answer 1

Given:

X, Y and Z are three equilateral triangles.

The side of X = 6 cm

The side of Y = 8 cm

Concept used:

Area of equilateral triangle = \(\frac{√3}{{4}}\)a2

Calculation:

Area of equilateral triangle = \(\frac{√3}{{4}}\)a2

F4 Madhri Defence 26-9-22 D1

According to the question

AX + AY = AZ

⇒ (\(\frac{√3}{{4}}\) × 62) + (\(\frac{√3}{{4}}\) × 82) = (\(\frac{\sqrt3}{{4}}\) × x2)

⇒ 36 + 64 = x2

⇒ 100 = x2

⇒ x = 10

∴ The side length of Z is 10 cm.