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
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Correct Answer: 270 cm2
Solution : Let the two sides of the right-angled triangle as $a$ and $b$, where $a > b$. Given that the hypotenuse is 39 cm and the difference of the other two sides is 21 cm. $⇒a^2 + b^2 = 39^2$ $⇒a^2 + b^2 = 1521$ ____(i) Also $a - b = 21$ $⇒a=21+b$ putting the value of $a$ in equation (i), we get, $⇒(21+b)^2 + b^2 = 1521$ $⇒441+42b+2b^2-1521=0$ $⇒b^2+21b-540=0$ $⇒(b+36)(b-15)=0$ $⇒b=15$ cm So, $a=21+b=21+15=36$ cm $\therefore$ The area of a right-angled triangle = $ \frac{1}{2}$ × base × height = $\frac{1}{2}$ × 36 × 15 = 270 cm2 Hence, the correct answer is 270 cm2.
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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 sides of a triangle are 20 cm, 21 cm, and 29 cm. The area of the triangle formed by joining the midpoints of the sides of the triangle will be:
Option 1: $67 \frac{2}{3}$ cm2
Option 2: $52 \frac{1}{2}$ cm2
Option 3: $47 \frac{1}{2}$ cm2
Option 4: $58 \frac{1}{3}$ cm2
Question : The base of a right prism is a right-angled triangle whose sides are 5 cm, 12 cm, and 13 cm. If the area of the total surface of the prism is 360 cm2, then its height is:
Option 1: 10 cm
Option 2: 12 cm
Option 3: 9 cm
Option 4: 11 cm
Question : The sides of a triangle are of length 8 cm, 15 cm, and 17 cm. Find the area of the triangle.
Option 1: 65 cm2
Option 2: 75 cm2
Option 3: 60 cm2
Option 4: 70 cm2
Question : Two triangles XYZ and UVW are congruent. If the area of $\triangle$XYZ is 58 cm2, then the area of $\triangle$UVW will be:
Option 1: 58 cm2
Option 2: 116 cm2
Option 3: 29 cm2
Option 4: 15 cm2
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