Question

In$△\mathbf{SUN}$ $\angle \mathbf{S}\cong \angle \mathbf{N}$,. Given that$\mathbf{SU}\mathbf{=}\mathbf{2}\mathbf{x}\mathbf{+}\mathbf{7}$ ,$\mathbf{UN}\mathbf{=}\mathbf{4}\mathbf{x}\mathbf{-}\mathbf{1}$ ,and$\mathbf{SN}\mathbf{=}\mathbf{3}\mathbf{x}\mathbf{+}\mathbf{4}$ , find the numerical length of each side.

Short answer

The numerical length of sides$SU$ ,$UN$ and$SN$ are 15,15 and 16 respectively.

Step-by-step solution

- Draw the possible diagram of the given problem.

The possible diagram of the given problem is:

It is being given that$\angle S\cong \angle N$.

The sides opposite to the equal angles are also equal.

As,$\angle S\cong \angle N$ , therefore the sides opposite to these angles are also equal.

That implies,$SU=UN$ .

- Find the value of x.

As,$SU=UN$, therefore it can be obtained that:

$\begin{array}{c}SU=UN\\ 2x+7=4x-1\\ 7+1=4x-2x\\ 8=2x\\ \frac{8}{2}=x\\ 4=x\end{array}$

Therefore, the value of x is 4.

- Find the numerical length of each sides.

Substitute 4 for x in the sides $SU$,$UN$ and $SN$.

Therefore, it can be obtained that:

$SU=2\left(4\right)+7=8+7=15$

$UN=4\left(4\right)-1=16-1=15$

$SN=3\left(4\right)+4=12+4=16$

Therefore, the numerical length of the sides$SU$ ,$UN$ and $SN$are 15,15 and 16 respectively.