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### Question

A room has a floor size of 17 × 31 sq. m. What is the height of the room if the sum of the areas of the base and roof is equal to the sum of the areas of the four walls?

**A**

$10{47/48}$ m.

**B**

$12{11/47}$ m.

**C**

$9{29/50}$ m.

**D**

$13{21/50}$ m.

**Soln.**

**Ans: a**

Let h be the height, and l and b be the length and breadth. We are given lb + lb = lh + hb + lh + hb. Combining the terms and cancelling 2, we get lb = h(l + b), which gives h = ${lb}/{l + b}$ = ${17 × 31}/{17 + 31}$ = ${527/48}$, which is same as: $10{47/48}$ m.