The two sides of a triangle are 40 cm and 41 cm. If the perimeter of the triangle is 90 cm, what is its area?
- A. 90 \text{ cm}^{2}
- B. 135 \text{ cm}^{2}
- C. 150 \text{ cm}^{2}
- D. 180 \text{ cm}^{2} ✓
Correct Answer: D. 180 \text{ cm}^{2}
Explanation
The third side of the triangle is 90 - (40 + 41) = 9 \text{ cm}. The sides are 9, 40, and 41. We can verify that 9^2 + 40^2 = 81 + 1600 = 1681 = 41^2. Since they form a Pythagorean triplet, the triangle is right-angled. Area = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 9 \times 40 = 180 \text{ cm}^2.
Related questions on Mensuration
- A pendulum swings through an angle of 30° and its end describes an arc of length 55 cm. What is the length of the pendulum? (Take $\pi = 22/...
- A conical tent has an angle of 60° at the vertex. If the curved surface area is 100 m^2, then what is the volume of the tent?
- A right circular cone and a hemisphere have equal base and equal volume. What is the ratio of the height of the cone to the radius of the he...
- A wire is in the form of an equilateral triangle with an area of 36\sqrt{3} cm^2. If it is changed into a semicircle, then what is its r...
- Let the area of the largest possible square inscribed in a circle of unit radius be x. Let the area of the largest possible circle inscribed...