Question

The area of a right-angled isosceles triangle whose hypotenuse is equal to $270m$ is :

• A. $19000m^2$
• B. $18225m^2$
• C. $17256m^2$
• D. $18325m^2$

Answer 1

The correct option is B

$18225m^2$

Explanation for the correct option:

Step 1:Finding the base and height of the triangle

Given hypotenuse $=270m$

Let $ABC$ be a right-angled triangle with hypotenuse $AC$.

An isosceles triangle has two sides equal.

So $AB=BC=a$

Since the triangle is a right-angled isosceles triangle, we use Pythagoras theorem

$$\begin{gathered} A{C}^2=A{B}^2+B{C}^2 \\ \Rightarrow {\left(270\right)}^2=a^2+a^2 \\ \Rightarrow 72900=2a^2 \\ \Rightarrow a^2=\frac{72900}{2} \\ \Rightarrow a^2=36,450 \end{gathered}$$

Thus, $a^2=36,450\Rightarrow a=\sqrt{36450}=190.9188$

$AB=BC=a=\sqrt{36450}=190.9188$

Step 2: Finding the area

We know that,

$\begin{array}{rcl}Areaoftriangle& =& \frac{1}{2}\times base\times height\\ & =& \frac{1}{2}\times AB\times BC\\ & =& \frac{1}{2}\times a\times a\\ & =& \frac{a^2}{2}\\ & =& \frac{36450}{2}\\ & =& 18225m^2\end{array}$

Thus, the area of the triangle is $18225m^2$

Hence option B is the correct option.