A geometry problem by Fidel Simanjuntak

Geometry Level 3

$\triangle P_1Q_1R_1$ is an isosceles right triangle. The green square is inscribed in $\triangle P_1Q_1R_1$ with area $1\space \text{cm}^2$ . Find the area of $\triangle P_1Q_1R_1$ to two decimal places ( in $\text{cm}^2$ ).

Try another problem on my set Let's Practice

The answer is 2.25.

2 solutions

A Former Brilliant Member
Apr 3, 2017

Let $b$ be the base and $h$ be the height of the triangle. In an isosceles right triangle, $b = 2h$ .

From the figure, we have

$tan~45 = \frac{1}{h-0.5}$ $\implies$ $h=1.5$

Solving for $b$ , we have

$b=2h=3$

Solving for the area of the triangle, we have

$A = \frac{1}{2}(3)(1.5)=$ $\boxed{\color{#D61F06}\large2.25~cm^2}$

Marta Reece
Apr 5, 2017

$1+\frac{1}{2}+\frac{1}{2}+\frac{1}{4}=2.25$

Nice way to solve the problem!!

Fidel Simanjuntak - 4 years, 2 months ago

A geometry problem by Fidel Simanjuntak

Try another problem on my set Let's Practice

The answer is 2.25.

2 solutions

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