Q58. - Algebra 2

Question

The following are the dimensions of four rectangles. Which rectangle has the same area as the triangle at the right?

$\begin{array}{cc}\left(A\right)1.6\text{ ft by }25\text{ ft}& \left(B\right)5\text{ ft by }16\text{ ft }\\ \left(C\right)3.5\text{ ft by }4\text{ ft }& \left(D\right)0.4\text{ ft by }50\text{ ft}\end{array}$

Step-by-Step Solution

Answer

Rectangle with dimension $\left(D\right)0.4\text{ ft by }50\text{ ft}$ has the same area as the given triangle.

Step 1 - Area of a triangle

Area A of a triangle having base b and height h is 

 $A=\frac{1}{2}\times b\times h$

Substitute 4 for b and 10 for h in this equation to get area of given triangle

$\begin{array}{l}A=\frac{1}{2}\times 4\times 10\\ A=20\text{ sq. ft}\end{array}$

Step 2 - Area of a rectangle

Area A of a rectangle having width w and length l is

 $A=wl$$A=wl$

Step 3 - Calculate area of rectangle with dimension given in option ( A )

Substitute $1.6\text{ ft}$ for w and $25\text{ ft}$ for l in the equation of area of rectangle

 $\begin{array}{c}A=1.6\times 25\\ A=40\text{ sq. ft}\end{array}$

Since, Area of rectangle is not equal to area of triangle 

Thus, option (A) is incorrect

Step 4 - Calculate area of rectangle with dimension given in option ( B )

Substitute $5\text{ ft}$ for w and $16\text{ ft}$ for l in the equation of area of rectangle

 $\begin{array}{c}A=5\times 16\\ A=80\text{ sq. ft}\end{array}$

Since, Area of rectangle is not equal to area of triangle 

Thus, option (B) is incorrect

Step 5 - Calculate area of rectangle with dimension given in option ( C )

Substitute $3.5\text{ ft}$ for w and $4\text{ ft}$ for l in the equation of area of rectangle

 $\begin{array}{c}A=3.5\times 4\\ A=14\text{ sq. ft}\end{array}$

Since, Area of rectangle is not equal to area of triangle 

Thus, option (C) is incorrect

Step 6 - Calculate area of rectangle with dimension given in option ( D )

Substitute $0.4\text{ ft}$ for w and $50\text{ ft}$ for l in the equation of area of rectangle

 $\begin{array}{c}A=0.4\times 50\\ A=20\text{ sq. ft}\end{array}$

Since, Area of rectangle is equal to area of triangle 

Thus, option (D) is correct.

Hence, correct option is (D).