Question : In an isosceles right-angled triangle, the perimeter is 30 m. Find its area (in m2). (Rounded off to the nearest integral value)
Option 1: 41
Option 2: 36
Option 3: 39
Option 4: 34
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Correct Answer: 39
Solution : The perimeter of right-angled isosceles triangle = 30 m Let the equal sides of the isosceles triangle be $a$ m. Hence, hypotenuse of the isosceles right angled triangle = $\sqrt{a^2+a^2}=\sqrt2a$ According to the question, $a+a+\sqrt2a=30$ ⇒ $a=\frac{30}{2+\sqrt2}$ ⇒ $a=15(2-\sqrt2)$ Area of isosceles right angle triangle = $\frac{1}{2}\times a^2$ = $\frac{1}{2}\times (15(2-\sqrt2))^2$ = $\frac{1}{2}\times 225\times (4+2-4\sqrt2)$ = $225\times(3-2\sqrt2)$ = $38.63$ m Hence, the correct answer is 39.
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Question : Find the area of a right-angled triangle whose base is 12 cm and the hypotenuse is 13 cm.
Option 1: 30 cm2
Option 2: 55 cm2
Option 3: 65 cm2
Option 4: 22 cm2
Question : The altitude drawn to the base of an isosceles triangle is 8 cm and its perimeter is 64 cm. The area (in cm2) of the triangle is:
Option 1: 240
Option 2: 180
Option 3: 360
Option 4: 120
Question : The hypotenuse of a right-angled triangle is 39 cm and the difference of the other two sides is 21 cm. Then, the area of the triangle is:
Option 1: 270 cm2
Option 2: 450 cm2
Option 3: 540 cm2
Option 4: 180 cm2
Question : In $\triangle ABC$, AB = BC = $k$, AC =$\sqrt2k$, then $\triangle ABC$ is a:
Option 1: Isosceles triangle
Option 2: Right-angled triangle
Option 3: Equilateral triangle
Option 4: Right isosceles triangle
Question : Find the area of a circle whose radius is equal to the side of a square whose perimeter is 196 m.
Option 1: 7457 m2
Option 2: 7546 m2
Option 3: 6477 m2
Option 4: 8844 m2
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