Question

the perimeter of the rectangle is 34 cm. the perimeter of the triangle is 30 cm. find the value of n. a. 10 cm b. 12 cm c. 14 cm d. 16 cm please select the best answer from the choices provided

Explanation:

Step1: Write the perimeter formula for the rectangle

The perimeter formula for a rectangle is $P = 2(m + n)$. Given $P=34$, so $2(m + n)=34$. Divide both sides by 2, we get $m + n=17$, then $m=17 - n$.

Step2: Write the perimeter formula for the triangle

The perimeter formula for the right - angled triangle is $P=m + n+(n + 1)$. Given $P = 30$, so $m + n+(n + 1)=30$.

Step3: Substitute $m$ into the triangle perimeter equation

Substitute $m = 17 - n$ into $m + n+(n + 1)=30$. We have $(17 - n)+n+(n + 1)=30$.
Simplify the left - hand side: $17 - n+n+n + 1=30$, which becomes $n+18 = 30$.

Step4: Solve for $n$

Subtract 18 from both sides of the equation $n+18 = 30$. We get $n=30 - 18=12$.

Answer:

B. 12 cm