Question : A rectangular carpet has an area of 120 m2 and a perimeter of 46 m. The length of its diagonal is:
Option 1: 23 m
Option 2: 13 m
Option 3: 17 m
Option 4: 21 m
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Correct Answer: 17 m
Solution : Let the length of the rectangle as $l$ and the width as $w$. The area of the rectangle, $lw = 120\ \text{m}^2⇒l=\frac{120}{w}$ The perimeter of the rectangle, $2(l + w) = 46\ \text{m}$ $⇒l + w = 23$ putting the value of $l$, we get, $\frac{120}{w}+w=23$ $⇒w^2-23w+120=0$ $⇒(w-8)(w-15)=0$ $⇒w=8,15$ If $w=8\ \text{m}$, then $l=15\ \text{m}$ If $w=15\ \text{m}$, then $l=8\ \text{m}$ $\therefore$ The length of the diagonal $= \sqrt{l^2 + w^2}=\sqrt{(8)^2 + (15)^2}= \sqrt{289}=17\ \text{m}$ Hence, the correct answer is 17 m.
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Question : The area of the rhombus is 216 cm2 and the length of its one diagonal is 24 cm. The perimeter (in cm) of the Rhombus is:
Option 1: 52
Option 2: 60
Option 3: 120
Option 4: 100
Question : If the sum of the dimensions of a rectangular parallelepiped is 24 cm and the length of the diagonal is 15 cm, then the total surface area is:
Option 1: 420 cm2
Option 2: 275 cm2
Option 3: 351 cm2
Option 4: 378 cm2
Question : What is the area of a triangular flower bed of a garden whose perimeter is 20 m and two sides are 5 m and 6 m?
Option 1: $10 \sqrt{2}$ m2
Option 2: $2 \sqrt{10}$ m2
Option 3: $5 \sqrt{2}$ m2
Option 4: $4 \sqrt{5}$ m2
Question : A square of side 3 cm is cut off from each corner of a rectangular sheet of length 24 cm and breadth 18 cm, and the remaining sheet is folded to form an open rectangular box. The surface area of the box is:
Option 1: 468 cm2
Option 2: 396 cm2
Option 3: 612 cm2
Option 4: 423 cm2
Question : The volume of air in a room is 204 m3. The height of the room is 6 m. What is the floor area of the room?
Option 1: 32 m2
Option 2: 46 m2
Option 3: 44 m2
Option 4: 34 m2
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