Question

The hypotenuse and base of a right triangle are 7.5 cm and 4.5 cm respectively. The measure of the perpendicular side will be:

• A. 5.5 cm
• B. 6 cm
• C. 6.5 cm
• D. 7 cm

Hint:

For right-angled triangles, use the Pythagoras theorem: \( c^2 = a^2 + b^2 \), where \( c \) is the hypotenuse and \( a \), \( b \) are the base and perpendicular sides.

Answer 1

The Correct Option is B

Step 1: Use the Pythagoras theorem.
In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Let the perpendicular side be \( x \). Then according to the Pythagoras theorem: \[ \text{Hypotenuse}^2 = \text{Base}^2 + \text{Perpendicular}^2 \] \[ 7.5^2 = 4.5^2 + x^2 \] \[ 56.25 = 20.25 + x^2 \] \[ x^2 = 56.25 - 20.25 = 36 \] \[ x = \sqrt{36} = 6 \, \text{cm} \] Thus, the measure of the perpendicular side is 6 cm. The correct answer is (B).