Question:
Mark (✓) against the correct answer:
The length of a rectangle is 8 cm and each of its diagonals measures 10 cm. The breadth of the rectangle is
(a) 5 cm
(b) 6 cm
(c) 7 cm
(d) 9 cm
Solution:
(b) $6 \mathrm{~cm}$
Let the breadth of the rectangle be $x \mathrm{~cm}$.
Diagonal $=10 \mathrm{~cm}$
Length $=8 \mathrm{~cm}$
The rectangle is divided into two right triangles.
Diagonal $^{2}=$ Length $^{2}+$ Breadth $^{2}$
$10^{2}=8^{2}+x^{2}$
$100-64=x^{2}$
$x^{2}=36$
$x=6 \mathrm{~cm}$
Breadth of the rectangle = 6 cm
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