## Geometry: Common Core (15th Edition)

$A = 138.72$
Two similar triangles have corresponding sides that are proportional. We know that the formula for the area of a rectangle is given as: $A = bh$, where $A$ is the area, $b$ is the base, and $h$ is the height. In $\triangle ABC$, $b = 4$, and $h = 3$. In $\triangle HIJ$, $b = x$ and $h = y$. We need to find the values for $x$ and $y$ to be able to find the area of this rectangle. Let's take a look at one set of corresponding sides that have given values. We can take a look at the hypotenuses of both triangles. Let's set up a proportion to relate two sets of corresponding sides in the two triangles to solve for one of the variables: $\frac{AC}{HJ} = \frac{AB}{HI}$ Let's plug in what we know: $\frac{5}{17} = \frac{4}{x}$ Use the cross products property to eliminate fractions: $5x = 68$ Divide both sides by $5$ to solve for $x$: $x = 13.6$ Let's set up the proportion to solve for $y$: $\frac{AC}{HJ} = \frac{BC}{IJ}$ Let's plug in what we know: $\frac{5}{17} = \frac{3}{y}$ Use the cross products property to eliminate fractions: $5y = 51$ Divide both sides by $5$ to solve for $x$: $y = 10.2$ Now that we have the values for $x$ and $y$, we can plug them into the formula to find the area of the rectangle: $A = (13.6)(10.2)$ Multiply to solve: $A = 138.72$