Question

The area of a rectangle is $40{\mathrm{cm}}^2$. If its length is $\left(2\mathrm{k}-5\right)\mathrm{cm}$ and its breadth is $8\mathrm{cm}$. Then, find the value of $\mathrm{k}$.

Answer 1

area of a rectangle $=\mathrm{length}\times \mathrm{breadth}$

Given, the area of a rectangle $=40{\mathrm{cm}}^2$

Length of rectangle $=\left(2\mathrm{k}-5\right)\mathrm{cm}$

Breadth of rectangle $=8\mathrm{cm}$

We know that area of a rectangle $=\mathrm{length}\times \mathrm{breadth}$

$$\begin{gathered} \therefore \left(2\mathrm{k}-5\right)\times 8=40 \\ \Rightarrow 16\mathrm{k}-40=40 \\ \Rightarrow 16\mathrm{k}=40+40 \\ \Rightarrow 16\mathrm{k}=80 \\ \Rightarrow \mathrm{k}=\frac{80}{16} \\ \Rightarrow \mathrm{k}=5 \end{gathered}$$

Hence, the value of $\mathrm{k}$ is $5$.