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Question : 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?

Option 1: 10 cm

Option 2: 10.5 cm

Option 3: 9.5 cm

Option 4: 9 cm


Team Careers360 19th Jan, 2024
Answer (1)
Team Careers360 24th Jan, 2024

Correct Answer: 10 cm


Solution :
X, Y, and Z are three equilateral triangles.
The side of X = 6 cm
The side of Y = 8 cm
Area of a equilateral triangle = $\frac{\sqrt{3}}{4}a^2$, where $a$ = side
According to the question,
Area X + Area Y = Area Z
$⇒ (\frac{\sqrt{3}}{4} \times 6^2) + (\frac{\sqrt{3}}{4} \times 8^2) = (\frac{\sqrt{3}}{4} \times x^2)$
$⇒ 36 + 64 = x^2$
$⇒ 100 = x^2$
$⇒ x = 10$ cm
Hence, the correct answer is 10 cm.

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