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SSC CHSL 2023 PYQ — Question 71

SSC CHSL - 13 March 2023 - Shift 2 • Quantitative Aptitude • Q71

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X, Y, and Z are three equalateral 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 length of Z?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 10 cm.

Let the length of Z = a

So, (34×62)+(34×82)=(34×a2)\left(\frac{\sqrt3}{4}\times 6^2\right)+\left(\frac{\sqrt3}{4}\times 8^2\right)=\left(\frac{\sqrt3}{4}\times a^2\right)

⇒ 93+163=3a249\sqrt3+16\sqrt3=\frac{\sqrt3a^2}{4}

 ⇒ 253=3a2425\sqrt3=\frac{\sqrt3a^2}{4}

⇒ a2/4 = 25

⇒ a2 = 100

⇒ a = 10

Hence, the length of Z is 10 cm.