# The base of an isosceles right triangle is 30 cm. Its area is - Mathematics

MCQ

The base of an isosceles right triangle is 30 cm. Its area is

#### Options

•  225 cm2

•  225 $\sqrt{3}$ cm

•  225 $\sqrt{2}$ cm

• 450 cm2

#### Solution

$\text{Let ABC be the right triangle in which} \angle B = 90° .$

$\text{ Now, base = BC; perpendicular = AB; Hypotenuse = AC }$

$\text{ Now, BC = 30 cm } \left( \text{ given } \right)$

$\text{ Now, ∆ ABC is an isosceles right angled ∆ and we know that hypotenuse is the longest side of the right ∆ }m.$

$\text{ So, AB = BC = 30 cm }$

$\text{ area of ∆ ABC } = \frac{1}{2} \times\text{ base } \times \text{ height }$

$= \frac{1}{2} \times BC \times AB$

$= \frac{1}{2} \times 30 \times 30$

$= 450 {cm}^2$

Concept: Application of Heron’s Formula in Finding Areas of Quadrilaterals
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 17 Heron’s Formula
Exercise 17.4 | Q 2 | Page 24

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