Question

Find the missing value from the given diagram

(a) 13 m
(b) 14 m
(c) 17 m
(d) 16 m

Answer 1

Hint: To solve this question, we will first name the figure, then we will consider any one of the triangle separated by a diagonal BD and then we will apply Pythagoras theorem in one of the triangle and hence obtain the measure of length of diagonal BD.

Complete step by step answer:
Now, let us see the properties of the rectangle and famous Pythagoras theorem before solving this problem.
A rectangle is a quadrilateral with four sides where opposite sides are equal and adjacent sides make a right angle that is an angle of ${{90}^{{}^\circ }}$ . Both diagonal rectangles are the same in length.
Let there be a right angled triangle, right angled at vertex B with height b and base a.

Then according to Pythagoras theorem,
The measure of hypotenuse that is length AC in figure is equal to $AC=\sqrt{{{a}^{2}}+{{b}^{2}}}$ .

Now, from the figure in question, we have length BC = 8 m and length DC = 15 m.
Clearly, it is a rectangle, so $\angle DCB={{90}^{{}^\circ }}$ .
So, we can apply Pythagoras theorem in triangle DCB, which is a right angled triangle at angle C.
So, according to Pythagoras theorem,
$BD=\sqrt{B{{C}^{2}}+D{{C}^{2}}}$
From, figure we have length BC = 8 m and length DC = 15 m.
So, $BD=\sqrt{{{8}^{2}}+{{15}^{2}}}$
We know that ${{8}^{2}}=64$ and ${{15}^{2}}=225$,
Substituting values of ${{8}^{2}}=64$ and ${{15}^{2}}=225$ in $BD=\sqrt{{{8}^{2}}+{{15}^{2}}}$, we get
$BD=\sqrt{64+225}$
$BD=\sqrt{289}$
We know that $\sqrt{289}=17$
So, BD = 17 m
Hence, option ( c ) is true.

Note:
Always remember the properties of the rectangle especially that adjacent sides make a right angle that is an angle of ${{90}^{{}^\circ }}$ as this is very helpful in solving questions. Also, remember that in right angled triangle, with base b and height a, $AC=\sqrt{{{a}^{2}}+{{b}^{2}}}$where AC is hypotenuse. Try to avoid calculation mistakes.