Question
Construct a rhombus ABCD in which diagonal $AC =5.8 cm$ and diagonal $BD =6.4 cm$.
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Answer
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Define the following term:
Cumulative frequency of a class
Cumulative frequency of a class
The internal dimensions of a rectangular box are $12 \ cm \times 9 \ cm$ . If the length of the longest rod that can be placed in this box is $17 \ cm$; find $x$.
→The area enclosed between two concentric circles is 770$cm ^2$. If the radius of the outer circle is 21 cm, calculate the radius of the inner circle.
[Hint. Let the radius of the inner circle be (21 - x) cm. Then
$\begin{array}{l}\pi(21)^2-\pi(21-x)^2=770 \Rightarrow x^2-42 x+245=0 \Rightarrow(x-35)(x-7)=0 . \\ \text { But, } x \neq 35 . \text { So, } x=7]\end{array}$
→[Hint. Let the radius of the inner circle be (21 - x) cm. Then
$\begin{array}{l}\pi(21)^2-\pi(21-x)^2=770 \Rightarrow x^2-42 x+245=0 \Rightarrow(x-35)(x-7)=0 . \\ \text { But, } x \neq 35 . \text { So, } x=7]\end{array}$
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Evaluate $: \frac{\cos 55^{\circ}}{\sin 35^{\circ}}+\frac{\cot 35^{\circ}}{\tan 55^{\circ}}$
→In the given figure, LMN is a right triangle in which $\angle M =90^{\circ}$, P and Q are mid-points of LM and LN respectively. If $LM =9 cm, MN =12 cm$ and $LN =15 cm$, find :
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(ii) the area of trapezium MNQP.
→(i) the perimeter of trapezium MNQP,
(ii) the area of trapezium MNQP.
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$(2 p-3 q)^3$
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If $a + 2b = 5;$ then show that $: a^3+ 8b^3+ 30ab = 125.$
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→