Q2. - Algebra 1

Question

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

Find the value of x so that the figures have the same area.

F $10$                                                   H $13$

G $12$                                                   J $15$

Step-by-Step Solution

Answer

The value of $x$ is $15$.

Step 1. Given information.

Both figures have the same area.

Step 2. To find equation by the both figures have same area.

The area of the rectangle is:  $(x-6)\times 25$

The area of the square is:  $15\times x$

Because both areas are same

So, $(x-6)\times 25=15\times x$

Step 3. To find the value of x

$\begin{array}{l}(x-6)\times 25=15\times x\\ \Rightarrow 25x-150=15x\\ \Rightarrow 25x-15x=150\\ \Rightarrow 10x=150\\ \Rightarrow x=15\end{array}$

Therefore, the value of $x$ is $15$.

Hence, the correct option is (F).