Question

In the given figure we have a square of side length 5 cm inscribed in a square of side length 7 cm, then find the values of ‘a’ and ‘b’.

• A. 2, 5
• B. 3, 4
• C. 1, 6
• D. None of the above

Answer 1

The correct option is B 3, 4

Given, PQRS is a square of side 7 cm.
From the figure we get that DS = b = (7-a) cm
Since, $\Delta$DSC is a right angled triangle, from pythagoras theorem we get
$D{S}^2+S{C}^2=D{C}^2$
$\Rightarrow a^2+(7-a{)}^2=5^2$
$\Rightarrow a^2+(7-a{)}^2=25$
when we substitute a = 1
$\Rightarrow a^2+(7-a{)}^2=1^2+6^2=37\ne 25$
So, a $\ne$ 1
when we substitute a = 2
$\Rightarrow a^2+(7-a{)}^2=2^2+5^2=29\ne 25$
So, a $\ne$ 2
when we substitute a = 3
$\Rightarrow a^2+(7-a{)}^2=3^2+4^2=25$
So, a = 3
$\therefore$ b = 7-a
= 4
Hence, a = 3 and b = 4.