1.  The area of a right-angled triangle is 40 times its base. What is its height ?

45 cm
60 cm
80 cm

```Answer

Answer: Option  C Explanation:△ = 1⁄2 * Base * Height
= 40 * Base = 1⁄2 * Base * Height
Height        = 80 cm.  ```

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2.  ABC is a triangle with base AB, D is a point on AB such that AB = 5 and DB = 3. What is the ratio of the area of △ ADC to the area of △ ABC ?

2 : 3
3 : 2
2 : 5
3 : 5

```Answer

Answer: Option  B Explanation:a =5, b = 12 and c = 13, So, s = 1⁄2(5 + 12 + 13) cm = 15 cm.
Area             = $\sqrt{\mathrm{15 * 10 * 3 * 2}}$ = 30 cm2.
1⁄2 * 12 * Height = 30.
Height        = 5 cm.    ```

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3.  If every side of a triangle is doubled, the area of the new triangle is K times the area of the old one. K is equal to :

$\sqrt{2}$
2
3
4

```Answer

Answer: Option  D Explanation:A1 = $\sqrt{3}$⁄2 a2 and A2 = $\sqrt{3}$⁄2(2a)2 = 4 * $\sqrt{3}$⁄2 a2 = 4A1.
K = 4. ```

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4.  If the area of an equilateral triangle is 24$\sqrt{3}$ sq. cm, then its perimeter is :

2$\sqrt{6}$ cm
4$\sqrt{6}$ cm
12$\sqrt{6}$ cm
96 cm

```Answer

Answer: Option  C Explanation:Area of an equilateral triangle of side a cm = ($\sqrt{3}$⁄4 a2) cm2.
$\sqrt{3}$⁄4 a2 = 24$\sqrt{3}$.
a2 = 96.
a  = 4$\sqrt{6}$.
Perimeter = 3a = 12$\sqrt{6}$cm. ```

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5.  The base of a triangular field is three times its altitude. If the cost of cultivating the field at Rs. 24.68 per hectare be Rs. 333.18, find its base and height.

200 m
250 m
300 m
350 m

```Answer

Answer: Option  C Explanation:Area of the field = Total cost⁄Rate = (333.18⁄24.68) hectares = 13.5 hectares.
= (13.5 * 10000) m2 = 135000 m2.
Let altitude   = x metres and base = 3x metres.
Then, 1⁄2 * 3x * x = 135000.
x2 = 90000.
x  =  300. ```

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