Q1. - 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.

Express the area of the triangle below as a monomial.

A $\mathbf{12}{\mathit{b}}^{\mathbf{5}}{\mathit{d}}^{\mathbf{7}}$

B $\mathbf{12}{\mathit{b}}^{\mathbf{6}}{\mathit{d}}^{\mathbf{10}}$

C $\mathbf{6}{\mathit{b}}^{\mathbf{6}}{\mathit{d}}^{\mathbf{10}}$

D $\mathbf{6}{\mathit{b}}^{\mathbf{5}}{\mathit{d}}^{\mathbf{7}}$

Step-by-Step Solution

Answer

The area of the given triangle in monomial is .$\mathbf{6}{\mathit{b}}^{\mathbf{5}}{\mathit{d}}^{\mathbf{7}}$Therefore, the option $\mathit{D}$ is correct.

Step 1. Write the formula for the area of the triangle.

The area ($A$) of the triangle is given by:

$A=\frac{1}{2}bh$

Where $b$ and $h$ are the base and height of the triangle respectively.

Step 2. Express the area of the given triangle below as a monomial.

The given diagram of the triangle is:

From the given diagram of the triangle, it can be noticed that the base and height of the triangle are $4b^3{d}^2$ and $3b^2{d}^5$ respectively.

Therefore, the values of $b$ and $h$ are $4b^3{d}^2$ and $3b^2{d}^5$ respectively.

Substitute the values of $b$ and $h$ in the formula of the area of the triangle.

Therefore, it is obtained that:

$\begin{array}{l}A=\frac{1}{2}bh\\ =\frac{1}{2}\left(4b^3{d}^2\right)\left(3b^2{d}^5\right)\\ =\frac{1}{2}\times 4\times 3\times b^3\times b^2\times d^2\times d^5\\ =\frac{12}{2}\times b^{3+2}\times d^{2+5}(\because a^m\times a^n=a^{m+n})\\ =6\times b^5\times d^7\\ =6b^5{d}^7\end{array}$

Therefore, the area of the given triangle in monomial is $6b^5{d}^7$. Therefore, the option $D$ is correct.